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How to Convert Scientific Notation to Standard Notation

Now we will take a closer look at how to convert from scientific notation back to standard notations. The main idea is to rewrite the power of 10, and then multiply the number a by this number.

Rule

Scientific Notation to Standard Notation

  • Calculate the power of 10 (ex. 104 = 10000).

  • Multiply the two numbers together.

Rule

Moving Comma Scientific Notation to Standard Notation

  • For large numbers, when n > 1 in 10n, you need to move the comma to the right to write it as a standard notation. The number will then be greater than 1.

  • For small numbers, when n < 0 in 10n, you need to move the comma to the left to write it as a standard notation. The number is then between 0 and 1.

Here are some examples where the power of 10 has a positive exponent. Keep in mind that the exponent is telling us how many decimal places to move the comma to the right. Note that it is the opposite way of what you did when you went from standard notation to scientific notation.

Example 1

Write 1.253 109 in standard notation.

1.253 109 = 1.253 1000000000 = 1253000000

1.253 109 = 1.253 1000000000 = 1253000000

Example 2

Write 6.24 105 in standard notation.

6.24 105 = 6.24 100000 = 624000

6.24 105 = 6.24 100000 = 624000

In the examples below, you can see how to proceed when a number in scientific notation has a negative exponent. You can imagine that the exponent tells us how many zeros there should be in total, or how many places you need to move the comma to the left. Note that it is the opposite of what you did when you went from standard notation to scientific notation.

Example 3

Write 6.24 105 as a standard notation.

6.24 105 = 6.24 0.00001 = 0.0000624

6.24 105 = 6.24 0.00001 = 0.0000624

Example 4

Write 1.982 103 in standard notation.

1.982 103 = 1.982 0.001 = 0.001982

1.982 103 = 1.982 0.001 = 0.001982

Example 5

Write 9.003 106 in standard notation.

9.003 106 = 9.003 0.000001 = 0.000009003

9.003 106 = 9.003 0.000001 = 0.000009003

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How to Calculate with Scientific Notation