Scientific Notation to Standard Notation
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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.
Quicklinks to...
- Parts of a Scientific Notation Expression
- What is Scientific Notation?
- Can we write any number in Scientific Notation?
- Why do we use Scientific Notation?
- How to Convert from Scientific Notation to Standard Notation
- Scientific Notation to Standard Notation Calculator
- Scientific Notation to Standard Notation Worked Examples
- Scientific Notation to Standard Notation Worksheets
- Scientific Notation to Standard Notation Quiz
- More Recommended Resources
Parts of a Scientific Notation Expression
- m is the coefficient which has an absolute value of at least 1 and less than 10. So 1 ≤ |m| < 10
- n is the exponent and is an integer, which can be positive, negative or zero
- 10 is the base
What is Scientific Notation?
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
- where m is a number which has an absolute value greater than or equal to 1 and less than 10.
- where n is an integer which can be positive or negative or zero.
These numbers are written in scientific notation:
- 2.7 x 104
- -8.2 x 10-2
- 5.1274 x 100
- 9 x 1015
- -8.7 x 10-8
These numbers are not written in scientific notation:
- 273 x 107 - the coefficient is greater than 10.
- 0.7 x 103 - the coefficient is less than 1
- 8 x 29 - the base needs to be 10, not 2
- 7.328 x 1000 - the base needs to be 10 and needs to have an exponent
- -0.3 x 10-2 - the coefficient is less than 1
Can we write any number using Scientific Notation?
Any number can be written in scientific notation except for 0.
Why do we use Scientific Notation?
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 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
Scientific Notation to Standard Notation Worksheets
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.
Convert Between Scientific Notation and Standard Notation Worksheets
These sheets involve converting numbers from scientific notation to standard notation and also from standard notation to scientific notation.
More Recommended Math Resources
Take a look at some more of our resources similar to our mm to inches conversion calculator.
Scientific to Standard Notation Calculators
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.
Standard Notation to Scientific Notation
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.
Convert to Scientific Notation Calculator
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.
More Number System Converters
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!
Scientific Notation to Standard Notation Online Quiz
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This quick quiz tests your skill at converting from scientific notation to standard notation.
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