Standard Notation to Scientific Notation Support Page

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.

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Parts of a Scientific Notation Expression

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 Standard Notation to Scientific Notation

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.

  • In the number 827372, the coefficient is 8.27372
  • In the number 0.0003082, the coefficient is 3.082
  • In the number -918283, the coefficient is -9.18283.
  • In the number -0.02165 the coefficient is -2.165.

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).

  • If we need to move the most significant digit to the right then we are making the number smaller, so we will have to multiply it by a power of 10 to bring it back to its proper value.
  • If we need to move the most significant digit to the left then we are making the number bigger, so we will have to divide it by a power of 10 to get back to its proper value.

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

  • where m is the coefficient and n is the exponent.

Lets look at some examples, or you can use our Convert to Scientific Notation Calculator and follow the steps there.

Standard Notation to Scientfic Notation Worked Examples

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.

  • The most significant digit is 7.
  • The coefficient will be 7.436

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 7436 needs to move 3 places to the right to be in the ones place.
  • This means that the exponent is 3.

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.

  • The most significant digit is 8.
  • The coefficient will be -8.945

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 8 in -894.5 needs to move 2 places to the right to be in the ones place.
  • The number of places is 2 places to the right, so the exponent is 2.

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.

  • The most significant digit is 6.
  • The coefficient will be 6.52

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 6 in 0.652 needs to move 1 places to the left to be in the ones place.
  • The number of places is 1 place to the left, so the exponent is -1

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.

  • The most significant digit is 9.
  • The coefficient will be 9

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 9 in -0.009 needs to move 3 places to the left to be in the ones place.
  • The number of places is 3 places to the left, so the exponent is -3.

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.

  • The most significant digit is 1.
  • The coefficient will be 1.2

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 1 in 12,000,000 needs to move 7 places to the right to be in the ones place.
  • The number of places is 7 places to the right, so the exponent is 7.

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.

  • The most significant digit is 7.
  • The coefficient will be 7.823 (it does not change)

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


Standard Notation to Scientific 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.

standard notation to scientific notation sheet 1 standard notation to scientific notation sheet 2

More Recommended Math Resources

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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.

Convert to Scientific Notation Calculator image

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.

Scientific Notation to Standard Notation Calculator image

Scientific Notation to Standard Notation Support

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.

Scientific Notation to Standard Notation image

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The calculators also show you detailed working out so you can see how to do it yourself!

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Standard Notation to Scientific Notation Online Quiz

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

 

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