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 : Convert the fraction part to a decimal Add the whole-number part to the result

Example

 Problem Convert  5 3/8 to a decimal. Procedure Convert the fraction part to a decimal 3/8 = 0.375 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 Divide:  4  ÷ 7 = 0.5714285  ... 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: Write a fraction that shows the decimal value as the numerator and 1 as the denominator. Continue multiplying the numerator and denominator by 10 until there is no longer a fraction part in the numerator. Reduce the result as necessary.

Example

 Problem Convert  0.25 to a fraction. Simplify and reduce as necessary. Procedure Write a fraction that shows the decimal value as the numerator and 1 as the denominator 0.25 = 0.25/1 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 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.