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How to work out recurring decimals

Want to find out how to work out recurring decimals? We've provided a step-by-step guide of how to work out recurring decimals to teach you everything you need to know.

Step 1: Count the number of recurring digits

For example, if we want to change 0.567567(567) ̅ to fraction, there are three recurring digits: 5,6, and 7.

Step 2: Convert to a fraction

We write the first set of the recurring digits as the numerator and the denominator with a series of 9s depending on the count from Step 1. Since we counted three and we have 567 as the numerator, denominator would have three 9’s.

Step 3: Simplify the fraction

Cancel common factors to simplify the fraction.

Examples of how to work out recurring decimals

Q1) Express the following recurring decimals to fractions.

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a. To change 0.123123(123) ̅ to a fraction, we first count the number of digits that are recurring.

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We would have three 9s on the denominator and 123 as the numerator.

0.(123) ̅=123/999

Look for common factors shared by the numerator and denominator to simplify the fraction.

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b. Now to change 0.5123123123(123) ̅, we first separate the recurring and nonrecurring digits.

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Express 0.5 as a fraction: .5= 5/10. To express 0.0(123) ̅ as a fraction, we can use the value of (123) ̅ from a. So, we have (123) ̅= 123/99=41/33.

Since there’s only 1 zero before the recurring digits, we multiply 41/33 by 1/10.

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Now, to find the value of 0.5(123) ̅, we combine the values of the decimals.

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