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  • Decimals: Division
  • 1-digit decimals by 10, 100 or 1,000

Decimals Workbook for Grades 5-6

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Dividing 1-digit decimals by 10, 100 or 1,000

Math worksheets: dividing 1-digit decimals by 10, 100 or 1,000.

Below are six versions of our grade 5 math worksheet on dividing 1-digit decimals by 10, 100 or 1,000. These worksheets are pdf files .

dividing decimals by 10 100 and 1000 problem solving

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Then, I also show this shortcut originates, using place value charts. In reality, the decimal point moving is sort of an illusion, and instead, the of the number move within the place value chart. This explanation can really help students to understand the reason behind the "trick" of moving the decimal point.


When you multiply whole numbers by 10, 100, 1000, and so on (powers of ten), you can simply “tag” as many zeros on the product as there are in the factor 10, 100, 1000 .

There is a for by numbers such as 10, 100, and 1000:

Move the decimal point to the as many places as there are zeros in the factor.

Move the decimal point one step to the right (10 has one zero).

Move the decimal point two steps to the right (100 has two zeros). The number 265. is 265 (as shown above).

1000 means we move the point three steps. Write a zero at the end of 0.37 so that the decimal point can “jump over to” that place.

1. Multiply.

Since 100 × 2 = 200, obviously the answer to
100 × 2.105 will be a little more than 200. Hence, you can just write the digits
2105 and put the decimal point so that the answer is 200-something:  .

2. Let's practice some more.

× 0

3. Now let's practice using powers of ten.

× 0.007 = _____________

× 2.01 = _____________

× 4.1 = ______________

× 41.59 = _____________

= ______________

= _____________

The (powers of ten) is similar. Can you guess it?

Move the decimal point to the for as many places (steps) as there are _________________________ in the factor 10, 100, or 1000.

Move the decimal point two steps to the ____________. You need to write zeros in front of the number.

          =  0.0056

Move the decimal point four steps to the ____________. You need to write zeros in front of the number.

 

   

   

5. Now let's practice using powers of ten.

= _____________

= _____________

= _____________

  = _____________

= _____________

= _____________

When 0.01 (a hundredth) is multiplied by ten, we get ten hundredths, which is equal to one tenth. Or, 10 × 0.01 = 0.1.

The entire number moved one “slot” to the left on the place value chart. This moving the decimal point in the number to the right.

 

A hundred times two tenths is like multiplying each tenth by 10, and by 10 again. Ten times two-tenths gives us two, and ten times that gives us 20.

Again, it is like moving the number over two “slots” to the left in the place value chart, or moving a decimal point in 0.2, two steps to the right.

 
When 3.915 is multiplied by 100, we get 391.5. Each part of the number (3, 9 tenths, 1 hundredth, 5 thousandths) is multiplied by 100, so each one of those moves two “slots” in the place value chart. This is identical to thinking that the decimal point moves two steps to the right.  

If we move the decimal point to solve 6 ÷ 100, we get:

6. Divide. Think of fractions to decimals, or use the shortcut. Compare the problems in each box!

  2
 =  
  2.1
 =  
  49
 =  
  490
 =  
  6
 =  
  6.5
 =  
  5
 =  
  5.04
 =  
  4.7
 =  
  4.7
 =  
  72
 =  
  72.9
 =  

7. A 10-lb sack of nuts costs $72.     How much does one pound cost?

8. Find the price of 100 ping-pong balls if one ping pong ball costs $0.89.

If we divide any by 1,000, the answer will have or decimal digits. This makes it easy to divide whole numbers by 1,000:  simply as your answer , and then make it have :

819,302
 = 819.302
41,300
 = 41.300 = 41.3
8,000
 = 8.000 = 8

Notice in the last two cases, we can simplify the results:  41.300 to 41.3 and 8.000 to 8.

9. Divide whole numbers by 1000. Simplify the final answer by dropping any ending decimal zeros.

  239
 =  
  35,403
 =  
  67
 =  
  263,000
 =  
  3,890
 =  
  1,692,400
 =  
  12,560,000
 =  
  9
 =  
  506,940
 =  

Similarly:

, copy the dividend and make it have . , copy the dividend and make it have .

72
  = 7.2
3,090
  = 30.90 = 30.9
74,992
  = 749.92
82,000
  = 8200.0 = 8,200

10. Divide whole numbers by 10 and 100.

  239
 =  
  89,803
 =  
  69
 =  
  239
 =  
  26,600
 =  
  23,133
 =  
  3,402
 =  
  9
 =  

12. Find one-hundredth of...

13. A pair of shoes that cost $29 was discounted by 3/10 of its price. What is the new price? ( Hint: First find 1/10 of the price. )

14. Find the discounted price:

      a. A bike that costs $126 is discounted by 2/10 of its price.

      b. A $45 cell phone is discounted by 5/100 of its price.              ( Hint: First find 1/100 of the price. )

15. One-hundredth of a certain number is 0.03. What is the number?  

16. Which vacuum cleaner ends up being cheaper? Model A, with the initial price $86.90, is discounted by 3/10 of its price.  Model B costs $75 now, but you will get a discount of 1/4 of its price.

In the problem  ____ ×  3.09  = 309, the number 3 becomes 300, so obviously
the missing factor is 100. You do not even have to consider the decimal point!

The same works with division, too. In the problem 7,209 ÷ _____ = 7.209, the missing divisor
is one thousand, because the value of the digit 7 was first 7000, and then it became 7.

17. It is time for some final practice. Find the missing numbers. Match the letter of each problem with the right answer in the boxes, and solve the riddle. There are two sets of boxes. The first boxes belong to the first set of exercises, and the latter boxes belong to the latter set.

Why didn’t 7 understand what 3.14 was talking about?

 ____ ×  0.04  = 40

  ____ × 9.381 = 938.1

1,000 × 4.20 =

 ____ ×  7.31  = 731

  ____ × 0.075 = 0.75

10 × 3.55 = ______

  100 × ______ = 4.2

1,000 × ______ = 355

____ × 60.15 = 60,150

4,200 1000   100 35.5 100 0.042   10   0.355 1000 1000
                       

  _____ ÷ 100 = 0.42

  _____ ÷ 10 = 2.3

 _____ ÷ 1000 = 4.2

   
  = 2.3 
   
  = 0.42 

O   4,360 ÷ _____ = 4.36

I    304.5 ÷ _____ = 3.045

230 100 10   23 1000 4.2 4,200 42
               

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dividing decimals by 10 100 and 1000 problem solving

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- the basic concept

Hint: it has to do with a "recipe" that many math lessons follow.
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Divide Decimals by 10, 100 or 1000

Related Pages Math Worksheets Lessons for Fourth Grade Free Printable Worksheets

Divide Decimals by 10, 100 or 1000 Worksheets

Printable “Divide Decimal” Worksheet: Divide Decimals by 10, 100, 1000 Divide Decimals by Whole Numbers (eg. 7.28 ÷ 4) Divide Decimals by Powers of 10 (eg. 74.2 ÷ 10 3 )

Divide Whole Numbers to give Decimal Quotients Divide Decimals by Whole Numbers (without rounding) Divide Decimals by Whole Numbers (with rounding) Divide Decimals by Decimals (with & without rounding)

In these free math worksheets, students practice how to divide decimals by 10, 100 or 1000.

How to divide decimals by 10, 100 or 1000?

To divide a decimal by 10, 100, or 1000, you can use the concept of moving the decimal point to the left by one, two, or three places respectively.

For example, let’s say you want to divide the decimal 2.5 by 10, 100, and 1000:

To divide 2.5 by 10, move the decimal point to the left by one place: 2.5 ÷ 10 = 0.25

To divide 2.5 by 100, move the decimal point to the left by two places: 2.5 ÷ 100 = 0.025

To divide 2.5 by 1000, move the decimal point to the left by three places: 2.5 ÷ 1000 = 0.0025

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Divide Decimals by 10, 100 or 1000 Worksheets .

Divide Decimals by 10, 100 or 1000

More Divide Decimals by 10, 100 or 1000 Worksheets

Printable Divide Decimals by 10, 100 or 1000 Worksheet (Answers on the second page.)

Online or Interactive Divide Decimals by Powers of 10 (Exponent Form) Divide Decimals by Multiples of 10

Generated Divide Decimals by 10, 100, 1,000

Divide Decimals by 10, 100 or 1000 Word Problems

3.2 million

170,000 km 2

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Dividing Decimals by 10 100 and 1000 Worksheets

Dividing decimals by 10 100 and 1000 worksheets introduce kids to the concept of dividing numbers containing different digits by 10, 100, or 1000. The problems could range from simple MCQ and fill in the blanks questions to tougher word problems.

Benefits of Dividing Decimals by 10 100 and 1000 Worksheets

By attempting the problems in dividing decimals by 10 100 and 1000 worksheets, kids can get an understanding of how to use this powerful concept to speed up their calculations while solving complicated sums.

In addition to this, the dividing decimals by 10 100 and 1000 worksheets have an answer manual consisting of detailed solutions to all questions. Students can refer to this if they require it.

Download Dividing Decimals by 10 100 and 1000 Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

Dividing Decimals by 10 100 and 1000 Worksheet - 1

Dividing Decimals by 10 100 and 1000 Worksheet - 2

Dividing Decimals by 10 100 and 1000 Worksheet - 3

Dividing Decimals by 10 100 and 1000 Worksheet - 4

  • Dividing a decimal by 10, 100, 1000

Dividing a decimal by 10, 100, or 1000 is done in the same way as dividing a decimal by a whole number. For example, divide 2.1 by 10. Solve this example with a column division:

20211

But there is a second way. It is easier. The essence of this method is that the point in the divisor is moved to the left by as many digits as there are zeros in the divisor.

Let's solve the previous example this way. 2,1 : 10. We look at the divisor. We are interested in how many zeroes are in it. We see that there is one zero. It means that in the divisor 2.1 we need to move the point to the left by one digit. We move the point to the left by one digit and see that there are no more digits left. In this case, we add another zero before the digit. As a result, we get 0.21

2.1 : 10 = 0.21

Let's try to divide 2.1 by 100. The number 100 has two zeros. So in the divisible 2.1 we have to move the point to the left by two digits:

2.1 : 100 = 0.021

Let's try to divide 2.1 by 1000. There are three zeros in the number 1000. So in the divisible 2.1 we have to move the point to the left by three digits:

2.1 : 1000 = 0.0021

Video lesson

  • Dividing a decimal by 0.1, 0.01, and 0.001
  • Dividing a decimal by a decimal

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DIVIDING DECIMALS by 10 100 and 1000 WORKSHEET

Problems 1-10 : Evaluate each of the following divisions.

Problem 1 :

Problem 2 :

209.3 ÷ 100

Problem 3 :

54002.7 ÷ 1000

Problem 4 :

18312.4 ÷ 10000

Problem 5 :

Problem 6 :

Problem 7 :

Problem 8 :

Problem 9 :

Problem 10 :

0.09 ÷ 1000

Problem 11 :

If 10 pencils cost $7.50, find the cost of one pencil.

Problem 12 :

If a man walks 3562.7 ft. of distance in 100 minutes, how many feet of distance will he walk in one minute?

Problem 13 :

A flight travels a distance of 7905.6 miles in 16 hours 40 minutes. Find the distance covered by the flight in one minute.

Problem 14 :

If the decimal number 943.Y7 is divided by 100, the answer is 9.4357. Find the value of Y.

tutoring.png

1. Answer :

Since we divide 27.9 by 10, we have to move the decimal point to the left by one digit.

27.9 ÷ 10  = 2.79

2. Answer :

Since we divide 209.3 by 100, we have to move the decimal point to the left by two digits.

209.3 ÷ 100 = 2.093

3. Answer :

Since we divide 54002.7 by 1000, we have to move the decimal point to the left by three digits.

54002.7 ÷ 1000 = 54.0027

4. Answer :

Since we divide 18312.4 by 10000, we have to move the decimal point to the left by four digits.

18312.4 ÷ 10000  = 1.83124

5. Answer :

Here 16 is divided by 10 and 16 is a whole number.

Since we divide 16 by 10, take decimal point in 16 such that there is one digit to the right of the decimal point.

16 ÷ 10  = 1.6

6. Answer :

Here 7 is divided by 10 and 7 is a whole number.

Since we divide 7 by 10, take decimal point in 7 such that there is one digit to the right of the decimal point.

7 ÷ 10  = 0 .7

7. Answer :

Here 99 is divided by 100 and 99 is a whole number.

Since we divide 99 by 100, take decimal point in 99 such that there are two digits to the right of the decimal point.

99 ÷ 100  = 0.99

8. Answer :

Since we divide 1.7 by 100, we have to move the decimal point to the left by two digits. But, we have only one digit to the left of the decimal point. To get one more digit, we have to add one zero.

1.7 ÷ 100  = 0.017

9. Answer :

Since we divide 0.65 by 10, we have to move the decimal point to the left by one digit. But, we have no digit to the left of the decimal point. To get one digit, we have to add one zero.

0.65 ÷ 10  = 0.065

10. Answer :

Since we divide 0.09 by 1000, we have to move the decimal point to the left by three digits. But, we have no digit to the left of the decimal point. To get three digits, we have to add three zeros.

0.09 ÷ 1000  = 0.00009

11. Answer :

To get the cost of one pencil. divide the total cost of 10 pencils by 10.

= ⁷⁵⁄₁₀  ÷  ¹⁰⁄₁

Change the division to multiplication by taking reciprocal of ¹⁰⁄₁ .

= ⁷⁵⁄₁₀  x  ⅒

=  ⁷⁵⁄ ₁₀₀

75 is a whole number. Since we divide 75 by 100, we have to take decimal point in 75such that there are two digits to the right of the decimal point.

The cost of one pencil is $0.75.

12. Answer :

To find the distance covered in one minute, we have to divide the distance covered in 100 minutes by 100.

= 3562.7/100

= 3562.7 ÷ 100

=  ³⁵⁶²⁷⁄₁₀  ÷  ¹⁰⁰⁄₁

Change the division to multiplication by taking reciprocal of ¹⁰⁰⁄₁ .

=  ³⁵⁶²⁷⁄₁₀  x  ¹⁄₁₀₀

=  ³⁵⁶²⁷⁄₁₀ ₀₀

35267 is a whole number. Since 35627 is divided by 1000, take decimal point in 35627 such that there are three digits to the right of the decimal point.

The man will walk 35.627 ft. of distance in one minute. 

13. Answer :

16 hours 40 minutes = (16 x 60) minutes + 40 minutes

= 960 minutes + 40 minutes

= 1000 minutes

Given :  7905.6  miles of distance covered in 16 hours 40 minutes.

16 hours 40 minutes ----> 7905.6 miles

1000 minutes ----> 7905.6 miles

1 minute ----> (7905.6/1000) miles

= 7905.6/1000

= 7905.6 ÷ 1000

=  ⁷⁹⁰⁵⁶⁄₁₀  ÷  ¹⁰⁰⁰⁄₁

Change the division to multiplication by taking reciprocal of ¹⁰⁰⁰⁄₁ .

=  ⁷⁹⁰⁵⁶⁄₁₀  x  ¹⁄₁₀₀₀

=  ⁷⁹⁰⁵⁶⁄₁₀ ₀₀₀

79056 i s a whole number. Since we divide 79056 by 10000, we have to take decimal point in 79056 such that there are four digits to the right of the decimal point.

The distance covered by the flight in one minute is 7.9056 ft.

14. Answer :

When we divide the decimal number 943.Y7 by 100, we have to move the decimal point to the left by two digits.

943.Y7 ÷ 100 = 9.43Y7 ----(1)

Given :  When 943.Y7 is divided by 100, the answer is 9.4357.

943.Y7 ÷ 100 = 9.4357 ----(1)

Comparing (1) and (2),

9.43Y7 = 9.4357

In the equality of two decimal numbers above, comparing the digits at thousandths places,

Practice Questions

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Multiply and divide decimals by 10, 100, and 1000

The rule or shortcut for multiplying and dividing decimals by 10, 100, and 1000 is really easy: you just move the decimal point as many steps as you have zeros in the power of ten. But do you know what this rule is based on? We look at that concept using PLACE VALUE CHARTS .

The rule says that if you're multiplying, you move the decimal point to the right (so as to make the number bigger), and vice versa for division. But in reality, it's not the POINT that is moving, but the NUMBER itself is moving within the different places. We can see this clearly by placing the number in a place value chart or table and considering what happens in the multiplication or division, place by place.

Multiply & divide decimals by powers of ten — online practice

Divide decimals with mental math: sharing divisions — video lesson

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Dividing Decimals by 10, 100, and 1000

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Multiplying & Dividing Decimals & Integers by 10, 100 & 1000

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Integers & Decimals - Multiplying & Dividing by 10, 100, 1000 - Spot the Mistake

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Integers & Decimals - Multiplying & Dividing by 10, 100, 1000 - Tarsia

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Integers & Decimals - Multiplying & Dividing by 10, 100, 1000 - Blockbusters

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dividing by 10, 100, 1000

By the end of this unit, students will be able to:

  • Understand the concept of dividing numbers by 10, 100, and 1000.
  • Perform divisions involving shifting the digits to the right by one, two, or three places.
  • Recognize the connection between these divisions and place value.
  • Apply the concept of dividing by powers of 10 to solve real-life and mathematical problems involving decimal fractions.

What's Included

  • Three-part Lesson
  • Self-marking Activities
  • Fluency, Reasoning and Problem-solving Questions.
  • Engaging Drag and Drop Activities
  • Interactive Self-marking Worksheet
  • Printable Worksheets to Consolidate Learning

Year 2 Mathematics:

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations, and arrays.

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common multiples

Common Multiples

short division without remainder

Short Divisions

rules of divisibility

Divisibility Rules

introduction to cube numbers

Cube Numbers

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How to Divide Decimals by 10 100 and 1000

Dividing decimals is like regular division, but with decimal points. First, if the divisor (the number you’re dividing by) has a decimal, move the decimal point to the right to make it a whole number. Then, move the decimal in the dividend (the number being divided) to the same number of places. After that, divide as usual, and place the decimal in the answer directly above where it appears in the dividend.

In this article, we will study dividing decimals, Decimals in every day life, how to divide decimals by 10,100,1000, how to Use Place Value Charts for Kids, and Applications of Dividing Decimals.

Table of Content

  • What is Dividing Decimals

Decimals in Everyday Life

  • How to divide decimals by 10,100,1000
  • How to Use Place Value Charts for Kids
  • Why Place Value Charts Work Well for Kids
  • Why is Dividing decimals important?
  • Important Tips:
  • Applications
  • Solved Examples
  • Practice Problems
  • Frequently Asked Questions FAQs

What are Decimal Numbers?

Decimal numbers are numbers that include a decimal point to represent a fraction or a part of a whole.

The decimal point separates the whole number part from the fractional part. Decimal numbers are based on the base-10 system, which means they use powers of 10.

Some of the common places in real life, where decimals are used are:

  • Money: When you buy something, the price often includes dollars and cents. For example, if a toy costs $5.75, the 0.75 is a decimal showing the cents.
  • Sports: In running or swimming races, times are recorded with decimals like 10.8 seconds or 15.3 seconds. The decimals show fractions of a second.
  • Measuring: Decimals are used when measuring things like height or length. If a pencil is 12.5 centimeters long, the 0.5 shows it’s a little more than 12 cm.
  • Baking and Cooking: Recipes sometimes ask for 0.5 cups of sugar or 1.25 teaspoons of salt. These decimals help get the right amount of ingredients.

What is Dividing Decimals?

Dividing decimals is when you split a number with a decimal point into equal parts.

Here’s an easy way to understand it:

  • Dividing by 10, 100, or 1000: When you divide a decimal by 10, 100, or 1000, the decimal point moves to the left.
Example: 4.5 ÷ 10 = 0.45 (Move the decimal one place left). Example: 4.5 ÷ 100 = 0.045 (Move the decimal two places left).
  • Dividing by whole numbers: When dividing by a regular number, you can first ignore the decimal and divide like usual. Then, put the decimal point back in the correct spot.
Example: 6.3 ÷ 3 = 2.1.

Place Value Chart

A Place Value Chart is a visual tool used in mathematics to help students understand the value of each digit in a number based on its position. The chart typically separates a number into columns, each representing a different place value, such as units, tens, hundreds, thousands, and so on.

Billions Hundred Millions Ten Millions Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Units Decimal Point Tenths Hundredths Thousandths
.

How to Divide Decimals by 10, 100, and 1000?

Dividing decimals by 10, 100, or 1000 is a simple process that involves shifting the decimal point to the left.

Dividing by 10

When you divide a decimal by 10, move the decimal point one place to the left.

  • Example: 34.56 ÷ 10 = 3.456

Dividing by 100

When you divide a decimal by 100, move the decimal point two places to the left.

  • Example: 34.56 ÷ 100 = 0.3456

Dividing by 1000

When you divide a decimal by 1000, move the decimal point three places to the left.

  • Example: 34.56 ÷ 1000 = 0.03456

Solved Examples: Dividing Decimals by 10 100 and 1000

Example 1: 35.8 ÷ 10

Move the decimal point 1 place to the left. 35.8 → 3.58 Answer: 35.8 ÷ 10 = 3.58

Example 2: 72.9 ÷ 100

Move the decimal point 2 places to the left. 72.9 → 0.729 Answer: 72.9 ÷ 100 = 0.729

Example 3: 456.7 ÷ 1000

Move the decimal point 3 places to the left. 456.7 → 0.4567 Answer: 456.7 ÷ 1000 = 0.4567

Example 4: 5 ÷ 100

Move the decimal point 2 places to the left. 5 → 0.05 Answer: 5 ÷ 100 = 0.05

Practice Problems on Divide Decimals by 10 100 and 1000

Problem 1: 35.6 ÷ 10 = ?

Problem 2: 0.42 ÷ 10 = ?

Problem 3: 156.78 ÷ 10 = ?

Problem 4: 54.2 ÷ 100 = ?

Problem 5: 0.357 ÷ 100 = ?

Problem 6: 7.2 ÷ 100 = ?

Problem 7: 78.45 ÷ 1000 = ?

Problem 8: 6.32 ÷ 1000 = ?

Problem 9: 923.1 ÷ 1000 = ?

To divide decimals by 10, 100, or 1000, simply move the decimal point to the left. The number of places you move it matches the number of zeros: For 10, move the decimal point 1 place left. For 100, move it 2 places left. For 1000, move it 3 places left. If there aren’t enough digits, add zeros to the left as needed. This makes dividing decimals by these numbers quick and easy!

  • Multiplying Decimals by 10, 100 and 1000
  • How to Divide Decimals by Whole Numbers

FAQs: Divide Decimals by 10 100 and 1000

What is the basic rule for dividing decimals by 10, 100, or 1000.

The basic rule is to move the decimal point to the left by as many places as there are zeros in the divisor: For 10, move the decimal point 1 place left. For 100, move the decimal point 2 places left. For 1000, move the decimal point 3 places left.

Does the decimal always have to be visible when dividing by 10, 100, or 1000?

Yes. Even if the decimal isn’t originally shown, it is assumed to be at the end of the number. For example: Dividing 25 by 10 (the decimal is after 25, i.e., 25.0), the result is 2.5.

How do you divide whole numbers by 10, 100, or 1000?

The same principle applies. Treat the whole number as having an invisible decimal at the end. For example: Dividing 500 by 100: Move the decimal 2 places left to get 5.00 or just 5.

What if I forget to move the decimal?

Forgetting to move the decimal results in an incorrect answer that is typically 10, 100, or 1000 times larger than the correct one.

How can I practice dividing decimals by 10, 100, or 1000?

Use worksheets or online tools, or even everyday examples like working with money (e.g., dividing prices) to practice.

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Decimals Worksheets

Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.

Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions.

Most Popular Decimals Worksheets this Week

Multiplying Various Decimals by 2-Digit Tenths

Grids and Charts Useful for Learning Decimals

dividing decimals by 10 100 and 1000 problem solving

General use decimal printables are used in a variety of contexts and assist students in completing math questions related to decimals.

The thousandths grid is a useful tool in representing decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.

  • Thousandths and Hundredths Grids Thousandths Grid Hundredths Grids ( 4 on a page) Hundredths Grids ( 9 on a page) Hundredths Grids ( 20 on a page)
  • Decimal Place Value Charts Decimal Place Value Chart ( Ones to Hundredths ) Decimal Place Value Chart ( Ones to Thousandths ) Decimal Place Value Chart ( Hundreds to Hundredths ) Decimal Place Value Chart ( Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Millions to Millionths )

Decimals in Expanded Form

dividing decimals by 10 100 and 1000 problem solving

For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart, and allow them to use it when converting standard form numbers to expanded form. There are actually five ways (two more than with integers) to write expanded form for decimals, and which one you use depends on your application or preference. Here is a quick summary of the various ways using the decimal number 1.23. 1. Expanded Form using decimals: 1 + 0.2 + 0.03 2. Expanded Form using fractions: 1 + 2 ⁄ 10 + 3 ⁄ 100 3. Expanded Factors Form using decimals: (1 × 1) + (2 × 0.1) + (3 × 0.01) 4. Expanded Factors Form using fractions: (1 × 1) + (2 × 1 ⁄ 10 ) + (3 × 1 ⁄ 100 ) 5. Expanded Exponential Form: (1 × 10 0 ) + (2 × 10 -1 ) + (3 × 10 -2 )

  • Converting Decimals from Standard Form to Expanded Form Using Decimals Converting Decimals from Standard to Expanded Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Form Using Fractions Converting Decimals from Standard to Expanded Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Factors Form Using Decimals Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Factors Form Using Fractions Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Exponential Form Converting Decimals from Standard to Expanded Exponential Form ( 3 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 4 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 5 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 6 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 7 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 8 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 9 Decimal Places)
  • Retro Converting Decimals from Standard Form to Expanded Form Retro Standard to Expanded Form (3 digits before decimal; 2 after) Retro Standard to Expanded Form (4 digits before decimal; 3 after) Retro Standard to Expanded Form (6 digits before decimal; 4 after) Retro Standard to Expanded Form (12 digits before decimal; 3 after)
  • Retro European Format Converting Decimals from Standard Form to Expanded Form Standard to Expanded Form (3 digits before decimal; 2 after) Standard to Expanded Form (4 digits before decimal; 3 after) Standard to Expanded Form (6 digits before decimal; 4 after)

Of course, being able to convert numbers already in expanded form to standard form is also important. All five versions of decimal expanded form are included in these worksheets.

  • Converting Decimals to Standard Form from Expanded Form Using Decimals Converting Decimals from Expanded Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Form Using Fractions Converting Decimals from Expanded Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Factors Form Using Decimals Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Factors Form Using Fractions Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Exponential Form Converting Decimals from Expanded Exponential Form to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 9 Decimal Places)
  • Retro Converting Decimals to Standard Form from Expanded Form Retro Expanded to Standard Form (3 digits before decimal; 2 after) Retro Expanded to Standard Form (4 digits before decimal; 3 after) Retro Expanded to Standard Form (6 digits before decimal; 4 after) Retro Expanded to Standard Form (12 digits before decimal; 3 after)
  • Retro European Format Converting Decimals to Standard Form from Expanded Form Retro European Format Expanded to Standard Form (3 digits before decimal; 2 after) Retro European Format Expanded to Standard Form (4 digits before decimal; 3 after) Retro European Format Expanded to Standard Form (6 digits before decimal; 4 after)

Rounding Decimals Worksheets

dividing decimals by 10 100 and 1000 problem solving

Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4.567 to the nearest tenth. First, truncate the number after the tenths place 4.5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4.6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6.959 to the nearest tenth. Truncate: 6.9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7.0. Watch that students do not write 6.10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...

We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6.5 --> 7; 3.555 --> 3.56; 0.60500 --> 0.61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5.5 would be rounded up to 6, but 8.5 would be rounded down to 8. The main reason for this is not to skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most pre-college students round up on a 5, that is what we have done in the worksheets that follow.

  • Rounding Decimals to Whole Numbers Round Tenths to a Whole Number Round Hundredths to a Whole Number Round Thousandths to a Whole Number Round Ten Thousandths to a Whole Number Round Various Decimals to a Whole Number
  • Rounding Decimals to Tenths Round Hundredths to Tenths Round Thousandths to Tenths Round Ten Thousandths to Tenths Round Various Decimals to Tenths
  • Rounding Decimals to Hundredths Round Thousandths to Hundredths Round Ten Thousandths to Hundredths Round Various Decimals to Hundredths
  • Rounding Decimals to Thousandths Round Ten Thousandths to Thousandths
  • Rounding Decimals to Various Decimal Places Round Hundredths to Various Decimal Places Round Thousandths to Various Decimal Places Round Ten Thousandths to Various Decimal Places Round Various Decimals to Various Decimal Places
  • European Format Rounding Decimals to Whole Numbers European Format Round Tenths to a Whole Number European Format Round Hundredths to a Whole Number European Format Round Thousandths to a Whole Number European Format Round Ten Thousandths to Whole Number
  • European Format Rounding Decimals to Tenths European Format Round Hundredths to Tenths European Format Round Thousandths to Tenths European Format Round Ten Thousandths to Tenths
  • European Format Rounding Decimals to Hundredths European Format Round Thousandths to Hundredths European Format Round Ten Thousandths to Hundredths
  • European Format Rounding Decimals to Thousandths European Format Round Ten Thousandths to Thousandths

Comparing and Ordering/Sorting Decimals Worksheets.

dividing decimals by 10 100 and 1000 problem solving

The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.

Students who have mastered comparing whole numbers should find comparing decimals to be fairly easy. The easiest strategy is to compare the numbers before the decimal (the whole number part) first and only compare the decimal parts if the whole number parts are equal. These sorts of questions allow teachers/parents to get a good idea of whether students have grasped the concept of decimals or not. For example, if a student thinks that 4.93 is greater than 8.7, then they might need a little more instruction in place value. Close numbers means that some care was taken to make the numbers look similar. For example, they could be close in value, e.g. 3.3. and 3.4 or one of the digits might be changed as in 5.86 and 6.86.

  • Comparing Decimals up to Tenths Comparing Decimals up to Tenths ( Both Numbers Random ) Comparing Decimals up to Tenths ( One Digit Differs ) Comparing Decimals up to Tenths ( Both Numbers Close in Value ) Comparing Decimals up to Tenths ( Various Tricks )
  • Comparing Decimals up to Hundredths Comparing Decimals up to Hundredths ( Both Numbers Random ) Comparing Decimals up to Hundredths ( One Digit Differs ) Comparing Decimals up to Hundredths ( Two Digits Swapped ) Comparing Decimals up to Hundredths ( Both Numbers Close in Value ) Comparing Decimals up to Hundredths ( One Number has an Extra Digit ) Comparing Decimals up to Hundredths ( Various Tricks )
  • Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths ( One Digit Differs ) Comparing Decimals up to Thousandths ( Two Digits Swapped ) Comparing Decimals up to Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Thousandths ( Various Tricks )
  • Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths ( One Digit Differs ) Comparing Decimals up to Ten Thousandths ( Two Digits Swapped ) Comparing Decimals up to Ten Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Ten Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Ten Thousandths ( Various Tricks )
  • Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths ( One Digit Differs ) Comparing Decimals up to Hundred Thousandths ( Two Digits Swapped ) Comparing Decimals up to Hundred Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Hundred Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Hundred Thousandths ( Various Tricks )
  • European Format Comparing Decimals European Format Comparing Decimals up to Tenths European Format Comparing Decimals up to Tenths (tight) European Format Comparing Decimals up to Hundredths European Format Comparing Decimals up to Hundredths (tight) European Format Comparing Decimals up to Thousandths European Format Comparing Decimals up to Thousandths (tight)

Ordering decimals is very much like comparing decimals except there are more than two numbers. Generally, students determine the least (or greatest) decimal to start, cross it off the list then repeat the process to find the next lowest/greatest until they get to the last number. Checking the list at the end is always a good idea.

  • Ordering/Sorting Decimals Ordering/Sorting Decimal Hundredths Ordering/Sorting Decimal Thousandths
  • European Format Ordering/Sorting Decimals European Format Ordering/Sorting Decimal Tenths (8 per set) European Format Ordering/Sorting Decimal Hundredths (8 per set) European Format Ordering/Sorting Decimal Thousandths (8 per set) European Format Ordering/Sorting Decimal Ten Thousandths (8 per set) European Format Ordering/Sorting Decimals with Various Decimal Places(8 per set)

Converting Decimals to Fractions and Other Number Formats

dividing decimals by 10 100 and 1000 problem solving

There are many good reasons for converting decimals to other number formats. Dealing with a fraction in arithmetic is often easier than the equivalent decimal. Consider 0.333... which is equivalent to 1/3. Multiplying 300 by 0.333... is difficult, but multiplying 300 by 1/3 is super easy! Students should be familiar with some of the more common fraction/decimal conversions, so they can switch back and forth as needed.

  • Converting Between Decimals and Fractions Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
  • Converting Between Decimals, Fraction, Percents and Ratios Converting Fractions to Decimals, Percents and Part-to-Part Ratios Converting Fractions to Decimals, Percents and Part-to-Whole Ratios Converting Decimals to Fractions, Percents and Part-to-Part Ratios Converting Decimals to Fractions, Percents and Part-to-Whole Ratios Converting Percents to Fractions, Decimals and Part-to-Part Ratios Converting Percents to Fractions, Decimals and Part-to-Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios with 7ths and 11ths

Adding and Subtracting Decimals

dividing decimals by 10 100 and 1000 problem solving

Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3.25 + 4.98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3.25 + 4.98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8.23)

  • Adding Tenths Adding Decimal Tenths with 0 Before the Decimal (range 0.1 to 0.9) Adding Decimal Tenths with 1 Digit Before the Decimal (range 1.1 to 9.9) Adding Decimal Tenths with 2 Digits Before the Decimal (range 10.1 to 99.9)
  • Adding Hundredths Adding Decimal Hundredths with 0 Before the Decimal (range 0.01 to 0.99) Adding Decimal Hundredths with 1 Digit Before the Decimal (range 1.01 to 9.99) Adding Decimal Hundredths with 2 Digits Before the Decimal (range 10.01 to 99.99)
  • Adding Thousandths Adding Decimal Thousandths with 0 Before the Decimal (range 0.001 to 0.999) Adding Decimal Thousandths with 1 Digit Before the Decimal (range 1.001 to 9.999) Adding Decimal Thousandths with 2 Digits Before the Decimal (range 10.001 to 99.999)
  • Adding Ten Thousandths Adding Decimal Ten Thousandths with 0 Before the Decimal (range 0.0001 to 0.9999) Adding Decimal Ten Thousandths with 1 Digit Before the Decimal (range 1.0001 to 9.9999) Adding Decimal Ten Thousandths with 2 Digits Before the Decimal (range 10.0001 to 99.9999)
  • Adding Various Decimal Places Adding Various Decimal Places with 0 Before the Decimal Adding Various Decimal Places with 1 Digit Before the Decimal Adding Various Decimal Places with 2 Digits Before the Decimal Adding Various Decimal Places with Various Numbers of Digits Before the Decimal
  • European Format Adding Decimals European Format Adding decimal tenths with 0 before the decimal (range 0,1 to 0,9) European Format Adding decimal tenths with 1 digit before the decimal (range 1,1 to 9,9) European Format Adding decimal hundredths with 0 before the decimal (range 0,01 to 0,99) European Format Adding decimal hundredths with 1 digit before the decimal (range 1,01 to 9,99) European Format Adding decimal thousandths with 0 before the decimal (range 0,001 to 0,999) European Format Adding decimal thousandths with 1 digit before the decimal (range 1,001 to 9,999) European Format Adding decimal ten thousandths with 0 before the decimal (range 0,0001 to 0,9999) European Format Adding decimal ten thousandths with 1 digit before the decimal (range 1,0001 to 9,9999) European Format Adding mixed decimals with Various Decimal Places European Format Adding mixed decimals with Various Decimal Places (1 to 9 before decimal)

Base ten blocks can be used for decimal subtraction. Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.

  • Subtracting Tenths Subtracting Decimal Tenths with No Integer Part Subtracting Decimal Tenths with an Integer Part in the Minuend Subtracting Decimal Tenths with an Integer Part in the Minuend and Subtrahend
  • Subtracting Hundredths Subtracting Decimal Hundredths with No Integer Part Subtracting Decimal Hundredths with an Integer Part in the Minuend and Subtrahend Subtracting Decimal Hundredths with a Larger Integer Part in the Minuend
  • Subtracting Thousandths Subtracting Decimal Thousandths with No Integer Part Subtracting Decimal Thousandths with an Integer Part in the Minuend and Subtrahend
  • Subtracting Ten Thousandths Subtracting Decimal Ten Thousandths with No Integer Part Subtracting Decimal Ten Thousandths with an Integer Part in the Minuend and Subtrahend
  • Subtracting Various Decimal Places Subtracting Various Decimals to Hundredths Subtracting Various Decimals to Thousandths Subtracting Various Decimals to Ten Thousandths
  • European Format Subtracting Decimals European Format Decimal subtraction (range 0,1 to 0,9) European Format Decimal subtraction (range 1,1 to 9,9) European Format Decimal subtraction (range 0,01 to 0,99) European Format Decimal subtraction (range 1,01 to 9,99) European Format Decimal subtraction (range 0,001 to 0,999) European Format Decimal subtraction (range 1,001 to 9,999) European Format Decimal subtraction (range 0,0001 to 0,9999) European Format Decimal subtraction (range 1,0001 to 9,9999) European Format Decimal subtraction with Various Decimal Places European Format Decimal subtraction with Various Decimal Places (1 to 9 before decimal)

Adding and subtracting decimals is fairly straightforward when all the decimals are lined up. With the questions arranged horizontally, students are challenged to understand place value as it relates to decimals. A wonderful strategy for placing the decimal is to use estimation. For example if the question is 49.2 + 20.1, the answer without the decimal is 693. Estimate by rounding 49.2 to 50 and 20.1 to 20. 50 + 20 = 70. The decimal in 693 must be placed between the 9 and the 3 as in 69.3 to make the number close to the estimate of 70.

The above strategy will go a long way in students understanding operations with decimals, but it is also important that they have a strong foundation in place value and a proficiency with efficient strategies to be completely successful with these questions. As with any math skill, it is not wise to present this to students until they have the necessary prerequisite skills and knowledge.

  • Horizontally Arranged Adding Decimals Adding Decimals to Tenths Horizontally Adding Decimals to Hundredths Horizontally Adding Decimals to Thousandths Horizontally Adding Decimals to Ten Thousandths Horizontally Adding Decimals Horizontally With Up to Two Places Before and After the Decimal Adding Decimals Horizontally With Up to Three Places Before and After the Decimal Adding Decimals Horizontally With Up to Four Places Before and After the Decimal
  • Horizontally Arranged Subtracting Decimals Subtracting Decimals to Tenths Horizontally Subtracting Decimals to Hundredths Horizontally Subtracting Decimals to Thousandths Horizontally Subtracting Decimals to Ten Thousandths Horizontally Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal
  • Horizontally Arranged Mixed Adding and Subtracting Decimals Adding and Subtracting Decimals to Tenths Horizontally Adding and Subtracting Decimals to Hundredths Horizontally Adding and Subtracting Decimals to Thousandths Horizontally Adding and Subtracting Decimals to Ten Thousandths Horizontally Adding and Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal

Multiplying and Dividing Decimals

dividing decimals by 10 100 and 1000 problem solving

Multiplying decimals by whole numbers is very much like multiplying whole numbers except there is a decimal to deal with. Although students might initially have trouble with it, through the power of rounding and estimating, they can generally get it quite quickly. Many teachers will tell students to ignore the decimal and multiply the numbers just like they would whole numbers. This is a good strategy to use. Figuring out where the decimal goes at the end can be accomplished by counting how many decimal places were in the original question and giving the answer that many decimal places. To better understand this method, students can round the two factors and multiply in their head to get an estimate then place the decimal based on their estimate. For example, multiplying 9.84 × 91, students could first round the numbers to 10 and 91 (keep 91 since multiplying by 10 is easy) then get an estimate of 910. Actually multiplying (ignoring the decimal) gets you 89544. To get that number close to 910, the decimal needs to go between the 5 and the 4, thus 895.44. Note that there are two decimal places in the factors and two decimal places in the answer, but estimating made it more understandable rather than just a method.

  • Multiplying Decimals by 1-Digit Whole Numbers Multiply 2-digit tenths by 1-digit whole numbers Multiply 2-digit hundredths by 1-digit whole numbers Multiply 2-digit thousandths by 1-digit whole numbers Multiply 3-digit tenths by 1-digit whole numbers Multiply 3-digit hundredths by 1-digit whole numbers Multiply 3-digit thousandths by 1-digit whole numbers Multiply various decimals by 1-digit whole numbers
  • Multiplying Decimals by 2-Digit Whole Numbers Multiplying 2-digit tenths by 2-digit whole numbers Multiplying 2-digit hundredths by 2-digit whole numbers Multiplying 3-digit tenths by 2-digit whole numbers Multiplying 3-digit hundredths by 2-digit whole numbers Multiplying 3-digit thousandths by 2-digit whole numbers Multiplying various decimals by 2-digit whole numbers
  • Multiplying Decimals by Tenths Multiplying 2-digit whole by 2-digit tenths Multiplying 2-digit tenths by 2-digit tenths Multiplying 2-digit hundredths by 2-digit tenths Multiplying 3-digit whole by 2-digit tenths Multiplying 3-digit tenths by 2-digit tenths Multiplying 3-digit hundredths by 2-digit tenths Multiplying 3-digit thousandths by 2-digit tenths Multiplying various decimals by 2-digit tenths
  • Multiplying Decimals by Hundredths Multiplying 2-digit whole by 2-digit hundredths Multiplying 2-digit tenths by 2-digit hundredths Multiplying 2-digit hundredths by 2-digit hundredths Multiplying 3-digit whole by 2-digit hundredths Multiplying 3-digit tenths by 2-digit hundredths Multiplying 3-digit hundredths by 2-digit hundredths Multiplying 3-digit thousandths by 2-digit hundredths Multiplying various decimals by 2-digit hundredths
  • Multiplying Decimals by Various Decimal Places Multiplying 2-digit by 2-digit numbers with various decimal places Multiplying 3-digit by 2-digit numbers with various decimal places
  • Decimal Long Multiplication in Various Ranges Decimal Multiplication (range 0.1 to 0.9) Decimal Multiplication (range 1.1 to 9.9) Decimal Multiplication (range 10.1 to 99.9) Decimal Multiplication (range 0.01 to 0.99) Decimal Multiplication (range 1.01 to 9.99) Decimal Multiplication (range 10.01 to 99.99) Random # Digits Random # Places
  • European Format Multiplying Decimals by 2-Digit Whole Numbers European Format 2-digit whole × 2-digit hundredths European Format 2-digit tenths × 2-digit whole European Format 2-digit hundredths × 2-digit whole European Format 3-digit tenths × 2-digit whole European Format 3-digit hundredths × 2-digit whole European Format 3-digit thousandths × 2-digit whole
  • European Format Multiplying Decimals by 2-Digit Tenths European Format 2-digit whole × 2-digit tenths European Format 2-digit tenths × 2-digit tenths European Format 2-digit hundredths × 2-digit tenths European Format 3-digit whole × 2-digit tenths European Format 3-digit tenths × 2-digit tenths European Format 3-digit hundredths × 2-digit tenths European Format 3-digit thousandths × 2-digit tenths
  • European Format Multiplying Decimals by 2-Digit Hundredths European Format 2-digit tenths × 2-digit hundredths European Format 2-digit hundredths × 2-digit hundredths European Format 3-digit whole × 2-digit hundredths European Format 3-digit tenths × 2-digit hundredths European Format 3-digit hundredths × 2-digit hundredths European Format 3-digit thousandths × 2-digit hundredths
  • European Format Multiplying Decimals by Various Decimal Places European Format 2-digit × 2-digit with various decimal places European Format 3-digit × 2-digit with various decimal places
  • Dividing Decimals by Whole Numbers Divide Tenths by a Whole Number Divide Hundredths by a Whole Number Divide Thousandths by a Whole Number Divide Ten Thousandths by a Whole Number Divide Various Decimals by a Whole Number

In case you aren't familiar with dividing with a decimal divisor, the general method for completing questions is by getting rid of the decimal in the divisor. This is done by multiplying the divisor and the dividend by the same amount, usually a power of ten such as 10, 100 or 1000. For example, if the division question is 5.32/5.6, you would multiply the divisor and dividend by 10 to get the equivalent division problem, 53.2/56. Completing this division will result in the exact same quotient as the original (try it on your calculator if you don't believe us). The main reason for completing decimal division in this way is to get the decimal in the correct location when using the U.S. long division algorithm.

A much simpler strategy, in our opinion, is to initially ignore the decimals all together and use estimation to place the decimal in the quotient. In the same example as above, you would complete 532/56 = 95. If you "flexibly" round the original, you will get about 5/5 which is about 1, so the decimal in 95 must be placed to make 95 close to 1. In this case, you would place it just before the 9 to get 0.95. Combining this strategy with the one above can also help a great deal with more difficult questions. For example, 4.584184 ÷ 0.461 can first be converted the to equivalent: 4584.184 ÷ 461 (you can estimate the quotient to be around 10). Complete the division question without decimals: 4584184 ÷ 461 = 9944 then place the decimal, so that 9944 is about 10. This results in 9.944.

Dividing decimal numbers doesn't have to be too difficult, especially with the worksheets below where the decimals work out nicely. To make these worksheets, we randomly generated a divisor and a quotient first, then multiplied them together to get the dividend. Of course, you will see the quotients only on the answer page, but generating questions in this way makes every decimal division problem work out nicely.

  • Decimal Long Division with Quotients That Work Out Nicely Dividing Decimals by Various Decimals with Various Sizes of Quotients Dividing Decimals by 1-Digit Tenths (e.g. 0.72 ÷ 0.8 = 0.9) Dividing Decimals by 1-Digit Tenths with Larger Quotients (e.g. 3.2 ÷ 0.5 = 6.4) Dividing Decimals by 2-Digit Tenths (e.g. 10.75 ÷ 2.5 = 4.3) Dividing Decimals by 2-Digit Tenths with Larger Quotients (e.g. 387.75 ÷ 4.7 = 82.5) Dividing Decimals by 3-Digit Tenths (e.g. 1349.46 ÷ 23.8 = 56.7) Dividing Decimals by 2-Digit Hundredths (e.g. 0.4368 ÷ 0.56 = 0.78) Dividing Decimals by 2-Digit Hundredths with Larger Quotients (e.g. 1.7277 ÷ 0.39 = 4.43) Dividing Decimals by 3-Digit Hundredths (e.g. 31.4863 ÷ 4.61 = 6.83) Dividing Decimals by 4-Digit Hundredths (e.g. 7628.1285 ÷ 99.91 = 76.35) Dividing Decimals by 3-Digit Thousandths (e.g. 0.076504 ÷ 0.292 = 0.262) Dividing Decimals by 3-Digit Thousandths with Larger Quotients (e.g. 2.875669 ÷ 0.551 = 5.219)

These worksheets would probably be used for estimating and calculator work.

  • Horizontally Arranged Decimal Division Random # Digits Random # Places
  • European Format Dividing Decimals with Quotients That Work Out Nicely European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number

In the next set of questions, the quotient does not always work out well and may have repeating decimals. The answer key shows a rounded quotient in these cases.

  • European Format Dividing Decimals by Whole Numbers European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number
  • European Format Dividing Decimals by Decimals European Format Decimal Tenth (0,1 to 9,9) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Hundredth (0,01 to 9,99) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Thousandth (0,001 to 9,999) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Ten Thousandth (0,0001 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Various Decimal Places (1,1 to 9,9999)

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IMAGES

  1. Year 6 Divide by 10, 100 and 1000 Decimals Reasoning and Problem

    dividing decimals by 10 100 and 1000 problem solving

  2. Dividing Decimals by 10, 100 and 1000 FREEBIE by Delta Teaching Resources

    dividing decimals by 10 100 and 1000 problem solving

  3. Multiplying and Dividing decimals by 10, 100, and 1000

    dividing decimals by 10 100 and 1000 problem solving

  4. multiplying and dividing decimals by 10 100 and 1000 worksheet

    dividing decimals by 10 100 and 1000 problem solving

  5. Numeracy: Dividing decimals by 10, 100 and 1000

    dividing decimals by 10 100 and 1000 problem solving

  6. Dividing Decimals by 10, 100 or 1,000

    dividing decimals by 10 100 and 1000 problem solving

VIDEO

  1. Dividing Decimals by 10 100 and 1000 (Easy)

  2. Multiplication of decimal numbers by 10,100 and 1000 || Planet Maths

  3. Dividing Decimals by Whole Numbers (79.8 ÷ 3) #shorts

  4. Dividing a Decimal Number with 1000 part 2

  5. multiplication and division of decimals by 10 100 and 1000

  6. Dividing By Multiples Of 10, 100, & 1,000

COMMENTS

  1. Dividing 1-digit decimals by 10, 100 or 1,000

    Below are six versions of our grade 5 math worksheet on dividing 1-digit decimals by 10, 100 or 1,000. These worksheets are pdf files. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6. Similar: Dividing 2-digit decimals by whole numbers Dividing whole numbers by 10, 100 or 1,000.

  2. Multiply and Divide Decimals by 10, 100, and 1000

    When you multiply whole numbers by 10, 100, 1000, and so on (powers of ten), you can simply "tag" as many zeros on the product as there are in the factor 10, 100, 1000 etc. Move the decimal point to the right as many places as there are zeros in the factor. Move the decimal point one step to the right (10 has one zero).

  3. Divide Decimals by 10, 100 or 1000

    To divide 2.5 by 10, move the decimal point to the left by one place: 2.5 ÷ 10 = 0.25. To divide 2.5 by 100, move the decimal point to the left by two places: 2.5 ÷ 100 = 0.025. To divide 2.5 by 1000, move the decimal point to the left by three places: 2.5 ÷ 1000 = 0.0025. Have a look at this video if you need to review how to divide ...

  4. Year 5 Divide by 10, 100 and 1,000 Reasoning and Problem Solving

    decimals by 10, 100 and 1000 Mathematics Year 5: (5F10) Solve problems involving number up to three decimal places ... Reasoning and Problem Solving Divide by 10, 100 and 1,000 Developing 1a. ÷ 100 2a. Aiden is correct, the place value grid shows 2.32. 3a. Each friend will get £132.50. Expected

  5. Multiplying and dividing decimals by 10, 100, 1000

    Keep going! Check out the next lesson and practice what you're learning:https://www.khanacademy.org/math/cc-fifth-grade-math/powers-of-ten/imp-multiplying-an...

  6. Divide decimals by 10, 100 and 1,000

    When you divide a decimal by 10, 100 and 1000, the place value of the digits decreases. The digits move to the right since the number gets smaller, but remember, the decimal point does not move.

  7. Dividing Decimals by 10 100 and 1000 Worksheets

    The problems could range from simple MCQ and fill in the blanks questions to tougher word problems. Benefits of Dividing Decimals by 10 100 and 1000 Worksheets. By attempting the problems in dividing decimals by 10 100 and 1000 worksheets, kids can get an understanding of how to use this powerful concept to speed up their calculations while ...

  8. PDF Dividing Decimals by 10, 100 and 1000

    Dividing Decimals by 10, 100 and 1000 Rules: To divide by 10, move each figure one place to the right. To divide by 100, move each figure two places to the right. To divide by 1000, move each figure three places to the right. Examples: 1) 31.2 ÷ 10 = 3.12 2) 754.2 ÷ 100 = 7.542 3) 52.3 ÷ 1000 = 0.0523

  9. Dividing a decimal by 10, 100, 1000

    In this case, we add another zero before the digit. As a result, we get 0.21. 2.1 : 10 = 0.21. Let's try to divide 2.1 by 100. The number 100 has two zeros. So in the divisible 2.1 we have to move the point to the left by two digits: 2.1 : 100 = 0.021. Let's try to divide 2.1 by 1000. There are three zeros in the number 1000.

  10. PDF Dividing Decimals by 10, 100 and 1000 Solutions

    Dividing Decimals by 10, 100 and 1000 Solutions Rules: To divide by 10, move each figure one place to the right. To divide by 100, move each figure two places to the right. To divide by 1000, move each figure three places to the right. Examples: 1) 31.2 ÷ 10 = 3.12 2) 754.2 ÷ 100 = 7.542

  11. DIVIDING DECIMALS by 10 100 and 1000

    DIVIDING DECIMALS by 10 100 and 1000. Consider the decimal number 25.86. Let us divide 25.86 by 10. = 25.86/10. Whenever a decimal number is divided by 10, the decimal point has to moved to left by one digit. = 2.586. In the similar manner, we can find the results, when a decimal number is divided by 100, 1000, etc.,

  12. DIVIDING DECIMALS by 10 100 and 1000 WORKSHEET

    10. Answer : Since we divide 0.09 by 1000, we have to move the decimal point to the left by three digits. But, we have no digit to the left of the decimal point. To get three digits, we have to add three zeros. 0.09 ÷ 1000 = 0.00009. 11. Answer : To get the cost of one pencil. divide the total cost of 10 pencils by 10.

  13. Multiply and divide decimals by 10, 100, and 1000

    Multiply and divide decimals by 10, 100, and 1000. The rule or shortcut for multiplying and dividing decimals by 10, 100, and 1000 is really easy: you just move the decimal point as many steps as you have zeros in the power of ten. ... the practice problems use an exponent, such as 0.245 × 10 5. We also look briefly at whole-number divisions ...

  14. PDF Year 6 Divide by 10, 100 and 1,000 Reasoning and Problem Solving

    with up 2 decimal places by 10, 100 and 1,000 with some use of zero. Greater Depth Solve a riddle with only one possible answer. Riddles involve dividing ... Reasoning and Problem Solving Divide by 10, 100 and 1,000 Developing 1a. A = 713.2; B = 71.4 (it cannot be made using the digit cards); C = 72.1 2a. Hafsa is correct. She has moved the

  15. Dividing Decimals by 10, 100, and 1000

    1) 910 10 a) 91 b) 0.91 c) 9.1 d) 9,100 2) 8,200 100 a) 820 b) 82 c) 8.2 d) 82,000 3) 25,000 1,000 a) 2,500 b) 250,000 c) 2.5 d) 25 4) 15 10 a) 150 b) 1,500 c) 1.5 d) 0.15 5) 2.4 10 a) 0.24 b) 24 c) 2,400 d) 0.024 6) 3.14 10 a) 31.4 b) 314 c) 0.0314 d) 0.314 7) 13 10 a) 0.13 b) 1.3 c) 130 d) 1,300 8) 4.1 10 a) 41 b) 410 c) 0.41 d) 0.041 9) 1.52 10 a) 15.2 b) 152 c) 0.0152 d) 0.152 10) 38 10 a ...

  16. Multiplying & Dividing Decimals & Integers by 10, 100 & 1000

    Place Value & Ordering Integers Multiplying & Dividing 1 & 2 Digit Integers Multiplying & Dividing 2 & 3 Digit Integers Calculations With Powers of 10 2-Minute Feedback Form

  17. PDF Year 5 Dividing by 10, 100 and 1,000 Reasoning and Problem Solving

    The calculation should be 32,000 ÷ 10 ÷ 10 ÷ 10 because the answer is 32. 8b. Dan has divided the number by 1,000 rather than 100. The correct answer is £27.40 not £2.74 9b. Various answers, for example: 30,600; 52,200; 41,400. Reasoning and Problem Solving - Dividing by 10, 100 and 1,000 ANSWERS.

  18. Dividing by 10, 100, 1000

    Understand the concept of dividing numbers by 10, 100, and 1000. Perform divisions involving shifting the digits to the right by one, two, or three places. Recognize the connection between these divisions and place value. Apply the concept of dividing by powers of 10 to solve real-life and mathematical problems involving decimal fractions.

  19. How to Divide Decimals by 10 100 and 1000

    Dividing decimals by 10, 100, or 1000 is a simple process that involves shifting the decimal point to the left. ... Practice Problems on Divide Decimals by 10 100 and 1000. Problem 1: 35.6 ÷ 10 ... measurements, and more advanced math concepts. To make decimals relatable, you can use everyday examples like money, where cents represent parts of ...

  20. Multiply and Dividing by 10, 100, 1000 etc Practice Questions

    Click here for Answers. . division, divide, multiplying, multiplication, powers of ten. Practice Questions. Previous: Division Practice Questions. Next: Enlargements Practice Questions. The Corbettmaths Practice Questions on Multiplying and Dividing by 10, 100, 1000 etc and also powers of ten.

  21. Year 5 Diving into Mastery: Step 11 Divide by 10, 100 and 1000

    This excellent diving into mastery teaching pack complements Version 3.0 of the White Rose Maths scheme of learning for year 5 Summer term Block 3 Decimals, Step 11: Divide by 10, 100 and 1000. Included in the pack is a time-saving PowerPoint containing various fluency, reasoning and problem-solving questions to use as a whole class. Place value charts and counters are used to support children ...

  22. PDF Year 5 Multiplying by 10, 100 and 1,000 Reasoning and Problem Solving

    Reasoning and Problem Solving Step 2: Multiply by 10, 100 and 1,000 National Curriculum Objectives: Mathematics Year 5: (5C6b) Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000 Differentiation: Questions 1, 4 and 7 (Problem Solving) Developing To calculate an answer based on 3 and 4 digit numbers multiplied by 10,

  23. Multiply and Divide by 10, 100, 1000 Word Problem Cards

    Check your KS2 class's knowledge and understanding of multiplying and dividing by 10, 100 and 1000 by using these word problem challenge cards. 11 problems featuring real life contexts will test how well your class understand the process of multiplying and dividing by 10, 100 and 1000. Referencing wider mathematical knowledge like converting measure and multi-step problem solving, these ...

  24. Decimals Worksheets

    Decimals Worksheets

  25. Y5 DiM: Step 10 Multiply by 10, 100 and 1,000 Teaching Pack

    This wonderful Diving into Mastery teaching pack complements Version 3.0 of the White Rose Maths scheme of learning for year 5 Summer term Block 3 Decimals, Step 10: Multiply by 10, 100 and 1,000. Included in the pack is a time-saving PowerPoint containing various fluency, reasoning and problem-solving questions to use as a whole class that will give children a secure understanding of place ...