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Chapter 4—Decimals
43 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 wholenumber 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 wholenumber 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 fractiontodecimal 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:  