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!

If you don't know fractions very well, you will probably struggle to do well on most math tests. Build a strong foundation in math today before it is too late!

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

Recent Articles

  1. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes