# Scientific Notation to Standard Notation Support Page

Welcome to our Scientific Notation to Standard Notation page.

This page will show you how to convert a range of numbers written in scientific notation to numbers in their standard form.

As well as step-by-step instructions, there are also worked examples and practice worksheets.

We also have an online quiz for you to test your skills with converting numbers in scientific notation back to standard notation.

Before you tackle scientific notation, you should be confident multiplying and dividing by 10 and 100.

### How to Convert Scientific Notation to Standard Notation

How to convert a number in scientific notation back to standard notation.

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

• if the exponent is negative then the coefficient will move to the right which will make it smaller (it will end up with an absolute value less than 1)
• if the exponent is positive then the coefficient will move to the left which will make it bigger - fill in any placeholders with zeros.
• if the exponent is zero, then the number will not change.

Lets look at some examples.

### Scientfic Notation to Standard Notation Worked Examples

#### Example 1) Convert 5.4 x 103 to standard notation.

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

The exponent is 3 so the coefficient needs to move 3 places to the left.

• One place to the left would be 54.
• Two places to the left would be 540.
• Three places to the left would be 5400.

So our final answer is 5.4 x 103 = 5400

#### Example 2) Convert 2.9 x 10-2 to standard notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

The exponent is -2 so the coefficient needs to move 2 places to the right.

• One place to the right would be 0.29
• Two places to the right would be 0.029

So our final answer is 2.9 x 10-2 = 0.029

#### Example 3) Convert -6 x 105 to standard notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

The exponent is 5 so the coefficient needs to move 5 places to the left.

• One place to the left would be -60
• Two places to the left would be -600
• 3 places to the left would be -6,000
• 4 places to the left would be -60,000
• 5 places to the left would be -600,000

So our final answer is -6 x 105 = -600,000

#### Example 4) Convert 9.243 x 10-4 to scientific notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

The exponent is -4 so we need to move the coefficient 4 places to the right.

• One place to the right would be 0.9243
• Two places to the right would be 0.09243
• 3 places to the right would be 0.009243
• 4 places to the right would be 0.0009243

So our final answer is 9.243 x 10-4 = 0.0009243

#### Example 5) Convert -3.7 x 100 to scientific notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

100 = 1 so this just has the effect of multiplying the coefficient by 1, so it stays the same value.

The exponent is 0 so we dont' need to move the coefficient at all.

So our final answer is -3.7 x 100 = -3.7 x 1 = -3.7

#### Example 6) Convert -3.7 x 100 to scientific notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

100 = 1 so this just has the effect of multiplying the coefficient by 1, so it stays the same value.

The exponent is 0 so we dont' need to move the coefficient at all.

So our final answer is -3.7 x 100 = -3.7 x 1 = -3.7

#### Example 7) Convert 6.35 x 101 to scientific notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

The exponent is 1 so we need to move the coefficient 1 places to the left.

101 = 10, so 6.35 x 101 = 6.35 x 10

• One place to the left would be 63.5

So our final answer is 6.35 x 101 = 63.5

#### Example 8) Convert 8 x 1012 to scientific notation

Step 1) The exponent tells us how many places to the left or right to move the coefficient.

The exponent is 8 so we need to move the coefficient 8 places to the left.

• One place to the left would be 80.
• Two places to the left would be 800.
• So 12 places to the left would be 8,000,000,000,000 (or 8 with 12 zeros).

So our final answer is 4.206 x 106 = 4,206,000

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### Scientific Notation to Standard Notation Online Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

This quick quiz tests your skill at converting from scientific notation to standard notation.

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