# Decimals to fractions

When converting decimals to fractions, it may be beneficial to apply the technique used to convert a number to scientific notation. Review then the lesson about scientific notation before starting this lesson.
By all means, do not start this lesson before reviewing scientific notation because I am going to make use of scientific notation.

0.06 = 6 × 10-2

Now, what is 10-2 equal to ?

Pay close attention to the following demonstration: Why 100 = 1 ? Please keep reading to see the explanation in the end of this lesson.

Since 0.06 = 6 × 10-2 , we get the following: Example #2:

Convert 0.014 to a fraction.

Follow all the steps above again. First, convert 0.014 to scientific notation.

0.014 = 14 × 10-3

10-2 = 1 / 102, so 10-3 = 1 / 103

In general, 10-n = 1 / 10n

14 × 10-3 = 14 × 1 / 103

14 × 10-3 = (14 / 1) × (1 / 103)

14 × 10-3 = (14 × 1) / (1 × 103)

14 × 10-3 = 14 / 103

14 × 10-3 = 14 / 1000

Notice that you could have gotten to the result a little faster bu using the shortcut below. However, we wanted to show you first all the steps again so you understand deeply! Example #3:

Convert 0.10252 to a fraction. First, convert 0.10252 to scientific notation.

0.10252 = 10252 × 10-5

10-5 = 1 / 105

10252 × 10-5 = 10252 × 1 / 105

10252 × 10-5 = (10252 / 1) × (1 / 105)

10252 × 10-5 = (10252 × 1) / (1 × 105)

10252 × 10-5 = 10252 / 105

10252 × 10-5 = 10252 / 1000

Once again, you could also just use the shortcut below: Why 100 = 1?

In order to see why 100 is equal to 1, we need to make the following two important observations:

Observation #1: 10n / 10n = 1

Observation #2: 10n / 10n = 10n-n = 100

Therefore, 10n / 10n = 1 = 10n-n = 100

1 = 100

## Decimals to fractions quiz. See how well you can convert a decimal to a fraction.

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