standard form homework answers

Standard Form: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

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Standard Form Worksheet and Answer Key

Students will practice working with the Standard Form Equation of a Line including finding the X and Y-intercept s, Graphing Standard Form Equations and converting Slope Intercept to Standard Form .

Example Questions

Find the x - and y - intercepts of the Standard Form Linear Equations below.

Write each equation in Standard Form using integer coefficients for A, B and C.

Graph each line using intercepts.

Other Details

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key
• Slope Intercept Form to Standard Form
• Slope Intercept to Standard Form
• Standard to Slope Intercept
• Equation of Line Formulas
• Linear Equation Links, Lessons and Tutorials
• Standard Form to Point Slope Form
• Point Slope to Standard Form

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

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GKT101: General Knowledge for Teachers – Math

Standard Form

When a linear equation is written in standard form, both variables x and y are on the same side of the equation. Watch this lecture series and practice converting equations to standard form.

Graph from linear standard form - Questions

We can graph the linear equation using these two points, as shown below:

GCSE Tutoring Programme

"Our chosen students improved 1.19 of a grade on average - 0.45 more than those who didn't have the tutoring."

In order to access this I need to be confident with:

This topic is relevant for:

Standard Form

Converting to and from Standard Form

Here we will learn how to convert to and from standard form , including how to adjust numbers to write them in standard form notation.

There are also converting to and from standard form worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is converting to and from standard form?

Converting to and from standard form is where we convert an ordinary number to a number written in standard form or scientific notation.

Standard form is a way of writing very large or very small numbers by comparing the powers of ten. Numbers in standard form are written in this format:

Where a is a number 1\leq{a}\lt10 and n is an integer.

Converting between ordinary numbers and numbers in standard form can help us to compare numbers and interpret answers given in standard form on a calculator. To do this we need to understand the place value of a number.

E.g. Let’s look at the number 350000 and place the digits in a place value table:

So 350000 written in standard form is:

How to convert ordinary numbers to standard form

In order to convert ordinary numbers to standard form:

• Identify the non-zero digits and write these as a decimal number which is \pmb{ 1\leq{x}\lt10} .
• In order to maintain the place value of the number, this decimal number needs to be multiplied by a power of ten.

Write the power of ten as an exponent.

Explain how to convert ordinary numbers to standard form

Standard form calculator worksheet

Get your free standard form calculator worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Converting ordinary numbers to standard form examples

Example 1: writing numbers in standard form with positive powers.

Write this number in standard form:

The non-zero digits need to be written in decimal notation.

The number needs to lie between 1\leq{x}\lt10

So the number will begin as 4.8… .

2 You now need to maintain the value of the number by multiplying that decimal by a power of ten. 

3 Write that power of ten as an exponent.

4 Write your number in standard form.

Example 2: writing numbers in standard form with positive powers

The number needs to lie between 1\leq{x}\lt10

So the number will begin as 5.42… .

You now need to maintain the value of the number by multiplying that decimal by a power of ten. 

Write that power of ten as an exponent.

Write your number in standard form.

Example 3: converting a small number to standard form

Write 0.00081 in standard form.

Identify the non-zero digits and write these as a decimal number which is \pmb{1\leq{x}\lt10}.

This number will begin with 8.1...

Identify what power of ten the decimal needs to be multiplied by in order to preserve place value .

8.1 \div 10000 = 0.00081

Example 4: converting a small number to standard form

Write 0.00718 in standard form.

Identify the non-zero digits and write these as a decimal number which is \pmb{{1\leq{x}\lt10}.}

The number will begin with 7.18…

7.8 \div 1000 = 0.0078

How to convert standard form to ordinary numbers

In order to convert from standard form to ordinary numbers:

• Convert the power of ten to an ordinary number
• Multiply the decimal number by this power of ten
• Write your number as an ordinary number

Explain how to convert standard form to ordinary numbers

Converting standard form to ordinary numbers examples

Example 5: converting standard form to an ordinary number.

Write 6.2\times10^4 as an ordinary number.

Write the exponent as a power of ten.

Multiply the decimal number by that power of ten.

Write your answer as an ordinary number.

Example 6: converting standard form to an ordinary number

Write 1.9\times10^{-3} as an ordinary number.

How to adjust numbers to standard form

Sometimes we might have a number that looks like it is in standard form however the decimal number is not between 1 and 10 , E.g. 36103 or 0.2104 . In this case we need to adjust the number.

In order to adjust numbers to standard form:

• Identify what power of ten the decimal number needs to be multiplied by so that the value is \pmb{1\leq{x}\lt10}.
• Apply the inverse of this to the power of ten.

Adjusting numbers to standard form examples

Example 7: adjusting number in standard form.

Write 48\times10^5 in standard form.

Identify what the first number needs to be multiplied or divided by so that it lies between \pmb{1\leq{x}\lt10}.

48 needs to be divided by 10 so 48 becomes 4.8 .

Apply the inverse operation to the power of ten.

10^5 needs to be multiplied by 10 which adds one to its power, so it becomes 10^6 .

Write your number in standard form. 

Example 8: adjusting numbers to standard form

Write 0.68\times10^{4} in standard form.

0.68 needs to be multiplied by 10 so it becomes 6.8 .

10^4 needs to be divided by 10 which subtracts one from its power, so it becomes 10^3 .

Example 9: adjusting numbers to standard form

Write 290\times10^{-4} in standard form.

290 needs to be divided by 100 so it becomes 2.9 .

10^{-4} needs to be multiplied by 100 which adds two to its power, so it becomes 10^{-2} .

Common misconceptions

• Writing a number with the incorrect power for a large or small number

This error is often made by counting the zeros following the first non zero digit for large numbers or zeros after the decimal point for small numbers, then writing this as the power, rather than considering the place value of the given number.

• Identifying incorrect place value with small numbers

In a number such as 0.000682 , selecting the ‘2’ to determine the exponent rather than the ‘6’ which has a higher place value. In standard form, this number would be 6.82 × 10^{-4} .

• Errors with negative numbers

When checking the standard form of a number, incorrectly adjusting the negative powers due to not applying negative numbers rules correctly. E.g. With small numbers, adding one to the power of 10^{-5} will result in 10^{-4} not 10^{-6} .

Related lessons

Converting to and from standard form is part of our series of lessons to support revision on standard form. You may find it helpful to start with the main standard form lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Standard form
• Multiplying and dividing in standard form
• Adding and subtracting in standard form

Practice standard form calculator questions

1. Write 270000 in standard form

The number between 1 and 10 here is 2.7.

2. Write 0.00079 in standard form

The number between 1 and 10 here is 7.9.

3. Write 6.1 \times 10^{4} as an ordinary number

4. Write 3.8 \times 10^{-5} as an ordinary number

5. Write 84\times10^{2} in standard form

This number is not in standard form as 84 is not between 1 and 10.

We need to divide 84 by 10 and, to compensate, multiply 10^2 by 10 , increasing the power by 1.

This gives us

6. Write 0.92\times10^{-5} in standard form

This number is not in standard form because 0.92 is not between 1 and 10.

We need to multiply 0.92 by 10 and, to compensate, divide 10^{-5} by 10 , decreasing the power by 1.

Standard form calculator GCSE questions

  (a)  Write 8.23\times10^{-6} , as an ordinary number.

(b)  Write the number 0.00702 in standard form.

(a)  0.00000823

(b)  7.02\times10^{-3}

(a)  The population of the USA is 3.3\times10^{8} , rounded to two significant figures.

Write this distance as an ordinary number.

(b) The population of Washington DC is 690000 rounded to two significant figures.

Write this number in standard form.

(a)  3 30000000 km

(b)  6.9\times10^{5}km

3.   Put the below numbers in order. Start with the smallest number.

0.092 \quad \quad 2.9\times10^{-3} \quad \quad 0.00029 \quad \quad 209\times10^{-4}

Converting all of the numbers to the same form or standard notation for comparison or 3 of the four numbers ordered correctly.

0.00029, \quad \quad 2.9\times10^{-3} , \quad \quad 209\times10^{-4}, \quad \quad 0.092

Learning checklist

You have now learned how to:

• Convert ordinary numbers standard form
• Convert standard form to ordinary numbers
• Adjust numbers to standard form notation

The next lessons are

• Linear equations
• Quadratic equations

Still stuck?

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Standard Form worksheets

Convert numbers to standard form, convert standard form to numbers, convert between ordinary numbers and standard form, adding in standard form, subtracting in standard form, add and subtract in standard form, multiply standard form, divide standard form, multiply and divide standard form, add, subtract, multiply and divide in standard form.

Standard Form

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Standard Form

What is "Standard Form"?

that depends on what you are dealing with!

I have gathered some common "Standard Form"s here for you..

Note: Standard Form is not the "correct form", just a handy agreed-upon style. You may find some other form to be more useful.

Standard Form of a Decimal Number

In Britain this is another name for Scientific Notation , where you write down a number this way:

In other countries it means "not in expanded form" (see Composing and Decomposing Numbers ):

Standard Form of an Equation

The "Standard Form" of an equation is:

(some expression) = 0

In other words, "= 0" is on the right, and everything else is on the left.

Example: Put x 2 = 7 into Standard Form

x 2 − 7 = 0

Standard Form of a Polynomial

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first (like the "2" in x 2 if there is one variable).

Example: Put this in Standard Form:

3 x 2 − 7 + 4 x 3 + x 6.

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x 6 + 4 x 3 + 3 x 2 − 7

Also, within each term, it is nice to have the variables in alphabetical order (if it does not make things more confusing):

yzx 2 + 4 yx 3

The highest degree is 3, so that goes first, also put the variables in alphabetical order

4 x 3 y + 3 x 2 yz

Standard Form of a Linear Equation

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

A shouldn't be negative, A and B shouldn't both be zero, and A , B and C should be integers.

Bring 3x to the left:

−3x + y = 2

Multiply all by −1:

3x − y = −2

Note: A = 3, B = −1, C = −2

Ax + By + C = 0

is sometimes called "Standard Form", but is more properly called the "General Form".

Standard Form of a Quadratic Equation

The "Standard Form" for writing down a Quadratic Equation is

( a not equal to zero)

Expand "x(x−1)":

x 2 − x = 3

Bring 3 to left:

x 2 − x − 3 = 0

Note: a = 1, b = −1, c = −3

Standard Form of a Circle Equation

With a circle like this:

The Standard Form is this:

(x−a) 2 + (y−b) 2 = r 2

See Circle Equations for more details.

Standard Form Textbook Exercise

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Standard form - homework

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

4 June 2024

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This homework is designed to support GCSE pupils learning of standard form. The exercise is suitable for all abilities and will help students retain the information learned from the lesson. I put these two topics together to fit in with Exam-boards scheme of work.

This resource will take students through writing standard and ordinary form as well as testing their ability on adding, subtracting, multiplying and dividing standard form. The homework offers questions that increase in difficulty allowing accessibility and challenge. Exam and more problem solver type questions are also included. The sheet also gives the students a chance to reflect on their learning.

Homework includes

Recall questions (previous topic) Topic skill questions Applied questions/ Exam questions Random problem solver Reflection page Solutions, solutions, solutions

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