Lesson 3
Converting Between Fractions and Decimals

 

Topic 1
Converting Fractions to Decimals

Procedure

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the denominator into the numerator.

Example

Problem

Convert 1/4 to a decimal.

Procedure

Divide: 1  � 4 = 0.25

Solution

1/4 = 0.25

Exercises

Convert fractions to decimals.

Topic 2
Converting Mixed Numbers to Decimals

Procedure

Converting Mixed  Numbers to Decimals

When converting a mixed number such as 2 3/4 :

  1. Convert the fraction part to a decimal
  2. Add the whole-number part to the result

Example

Problem

Convert  5 3/8 to a decimal.

Procedure
  1. Convert the fraction part to a decimal
3/8 = 0.375
  1. Add the whole-number part to the result
5 +  0.375 = 5.375
Solution

5  3/8 = 5.375

Exercises

Convert mixed numbers to decimals.

When converting fractions to decimals, you often find situations where there seems to be no end to the number of decimal places. For example, you will never find the end of the decimals when converting 2/3 to a decimal fraction. Try it:

2 � 3 = 0.6666666666...

It goes on for ever and ever. This is handled by rounding the decimal to a given place. Rounding this example to the thousandths place, we get 2 � 3 = 0.667.

Example

Problem

Convert 4/7 to a decimal. Round to the nearest hundredth.

Procedure

  1. Divide:  4  � 7 = 0.5714285  ...
  2. Round to the nearest hundredth: 0.57
Solution

4/7 = 0.57

Exercises

Convert these fractions to decimal values. Round to the nearest hundredth (two decimal places) when necessary.

Topic 3
Converting Decimals to Fractions

 

Procedure

To convert a decimal to a fraction:

  1. Write a fraction that shows the decimal value as the numerator and 1 as the denominator.
  2. Continue multiplying the numerator and denominator by 10 until there is no longer a fraction part in the numerator.
  3. Reduce the result as necessary.

Example

Problem

Convert  0.25 to a fraction. Simplify and reduce as necessary.

Procedure

  1. Write a fraction that shows the decimal value as the numerator and 1 as the denominator

0.25 = 0.25/1

  1. Continue multiplying the numerator and denominator by 10 until there is no longer a fraction portion in the numerator.

 0.25/1 = 2.5/10 = 25/100

  1. Reduce the result as necessary.

25/100 = 1/4

Solution

0.25 = 1/4

Exercises

Convert these decimals to fractions. Simplify and reduce as necessary.

If you are having any trouble understanding the content of this lesson, you will benefit from a more detailed tutorial on the subject.