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Chapter 4—Decimals

4-3 Converting Between Fractions and Decimals

 When you complete the work for this section, you should be able to: Convert any fraction or mixed number to a decimal value. Convert any decimal fraction to a fraction or mixed number.

Converting Fractions to Decimals

 Procedure Converting Fractions to Decimals To convert a fraction to a decimal, divide the denominator into the numerator.

Example 1

 Problem Convert 1/4 to a decimal. Procedure Divide 1  ÷ 4 = 0.25 Solution 1/4 = 0.25

Examples and Exercises

 Converting Fractions to Decimals Use these interactive examples and exercises to strengthen your understanding and build your skills:

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

Examples and Exercises

 Converting Mixed Numbers to Decimals Use these interactive examples and exercises to strengthen your understanding and build your skills:

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.

Actually, most fraction-to-decimal conversions turn out that way, and you have to end the conversion somehow. And how's that? By rounding the decimal at some place value. So if we decide to round 2 ÷ 3 to the thousandths place, we get 2 ÷ 3 = 0.667. Close enough.

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

Examples and Exercises

 Converting Fractions to Decimals (With Rounding) Convert these fractions to decimal values. Round to the nearest hundredth (two decimal places) when necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills:

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

Examples and Exercises

 Converting Decimals to Fractions Convert these decimals to fractions. Simplify and reduce as necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills:

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