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.
Scientific notation is a special way of writing numbers.
Scientific notation is also called standard index form, or standard form in the UK.
Numbers in scientific notation are written in the form:
m x 10n
These numbers are written in scientific notation:
These numbers are not written in scientific notation:
Any number can be written in scientific notation except for 0.
Scientific Notation is especially useful when writing numbers that are too large, or too small, to be written easily in standard notation.
Example: 280,000,000 is written as 2.8 x 108
Example: 0.000000000132 is written as 1.32 x 10-10
Example: the mass of the sun is 1.989 x 1030 kg. This is the same as 1,989,000,000,000,000,000,000,000,000,000 kg.
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.
Lets look at some examples.
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.
So our final answer is 5.4 x 103 = 5400
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.
So our final answer is 2.9 x 10-2 = 0.029
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.
So our final answer is -6 x 105 = -600,000
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.
So our final answer is 9.243 x 10-4 = 0.0009243
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
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
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
So our final answer is 6.35 x 101 = 63.5
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.
So our final answer is 4.206 x 106 = 4,206,000
We have created 2 worksheets for you to practice this skill.
The sheets are at a similar level of difficulty, though the second sheet involves trickier numbers to convert.
These sheets involve converting numbers from scientific notation to standard notation and also from standard notation to scientific notation.
Take a look at some more of our resources similar to our mm to inches conversion calculator.
This calculator will take a number in scientific notation and convert it into standard notation.
It can take numbers with exponents between -30 and 30.
We also have a page dedicated to converting numbers from standard notation to scientific notation.
There are step-by-step instructions and lots of worked examples to look at.
There are also practice worksheets to try out.
Our Convert to scientific notation calculator will take a number and convert it to scientific notation and e-notation.
It shows you all the working out along the way too.
Our number system converters will convert numbers from binary, octal or hexadecimal into decimal (or from decimal to binary, octal or hex).
The calculators also show you detailed working out so you can see how to do it yourself!
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.
For more information on the information we collect, please take a look at our Privacy Policy
We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.
This quick quiz tests your skill at converting from scientific notation to standard notation.
How to Print or Save these sheets
Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!
How to Print or Save these sheets
Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!
The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.
We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.
New! Comments
Have your say about the Math resources on this page! Leave me a comment in the box below.