How to Convert Repeating Decimals Into Fractions
The way we display numbers can change the course of a presentation or plan. A decimal can be expressed as either exact -- 0.14, for example -- or recurring -- 0.45454545. Converting a recurring decimal into a fraction can be done using basic algebra to move the decimal point and find a denominator for the fraction.
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Instructions
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Put the decimal into algebraic terms. Using the example of the recurring decimal 0.4545454545, let x = 0.4545454545.
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Move the decimal so the first recurring number is before the decimal point. In this case that means that you need to multiply it by 100. So 100x = 45.45454545.
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Remove the decimal numbers. Subtract x from 100x. So 100x - x = 45. Thus, 99x = 45
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Isolate x on one side of the equation. You are left with the fraction for 0.4545454545, x = 45/99
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