Converting recurring decimals to fractions and vice versa

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How to convert a recurring decimal into a fraction

Example 1

Write  0.77..   as a fraction in it's lowest terms.

Our first step is to form a simple equation where  x=0.77... By multiplying both sides by 10 we can obtain another equation with 10x=7.77... Now we eliminate the recurring part of the decimal by subtracting x from 10x.

x10x9xx=0.77..=7.77..=7=79 So we have our answer 0.77...=79.

The important part to remember is to get two equations in x


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