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.
Let's start with an example. Convert 0.06 to a fraction.

0.06 = 6 × 10-2

Now, what is 10-2 equal to ?

Pay close attention to the following demonstration:

decimals to fractions

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:
The decimal 0.06 to fraction

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!

The decimal 0.014 to fraction

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:

0.10252 written as a fraction

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.



Still struggling with fractions? Get rid of your fears and frustrations once and for all!

Buy my ebook. It offers a thorough coverage of fractions!


Fractions ebook cover

Recent Articles

  1. Introduction to Physics

    Nov 18, 20 01:20 PM

    Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.