Welcome to our Standard Notation to Scientific Notation page.
This page will show you how to convert a range of numbers to scientific notation.
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 to scientific 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 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
The most significant digit is the first (non-zero) digit that the number has.
In the number 827372, the most significant digit is 8.
In the number 0.0003082, the most significant digit is 3.
When the most significant digit is in the ones place, the coefficient will have an absolute value greater than or equal to 1 and less than 10 which is what we need.
The digits to the right of the most significant digit will come after the decimal point.
If the number is negative, then the coefficient will be negative.
Step 2) Find how many places the number needs to move (left or right) for the most significant digit to be in the ones place.
The number of places we need to move the number tells us the exponent (or order of magnitude needed).
The amount that we need to multiply (or divide) the number by is 10n, where n is the number of places we need to move the digit.
If we are dividing the number by 10n, then this is the same as multiplying the number by 10-n.
So if the original number has an absolute value less than 1 to start with then the exponent will be negative.
This also means that if we need to move the most significant digit to the left then the exponent will be negative.
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
Our final answer will be m x 10n
Lets look at some examples, or you can use our Convert to Scientific Notation Calculator and follow the steps there.
Example 1) Convert 7436 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
Step 2) Find how many places the most significant digit needs to move (left or right) so that it is in the ones place.
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
So our final answer is 7436 = 7.436 x 103
Example 2) Convert -894.5 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
Step 2) Find how many places the most significant digit needs to move (left or right) so that it is in the ones place.
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
So our final answer is -894.5 = -8.945 x 102
Example 3) Convert 0.652 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
Step 2) Find how many places the most significant digit needs to move (left or right) so that it is in the ones place.
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
So our final answer is 0.652 = 6.52 x 10-1
Example 4) Convert -0.009 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
Step 2) Find how many places the most significant digit needs to move (left or right) so that it is in the ones place.
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
So our final answer is -0.009 = -9 x 10-3
5) Convert 12,000,000 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
Step 2) Find how many places the most significant digit needs to move (left or right) so that it is in the ones place.
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
So our final answer is 12,000,000 = 1.2 x 107
6) Convert 7.823 to scientific notation
Step 1) Find the coefficient by rewriting the entire number with the most significant digit in the ones place.
Step 2) Find how many places the most significant digit needs to move (left or right) so that it is in the ones place.
The 7 in 7.823 is already in the ones place so it does not need to move.
The number of places is 0 places to the right, so the exponent is 0.
Step 3) Find the coefficient by moving the entire number by the same number of places as the significant digit.
Moving the number 0 places to the right gives us a coefficient of 7.823
Step 3) Rewrite the number as the coefficient multiplied by the base 10 exponent.
So our final answer is 7.823 = 7.823 x 100
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.
Take a look at some more of our resources similar to our mm to inches conversion 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.
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 scientific notation to standard notation.
There are step-by-step instructions and lots of worked examples to look at.
There are also practice worksheets to try out.
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!
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This quick quiz tests your skill at converting from standard notation to scientific notation.
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