Converting Recurring Decimals to Fractions

This page provides a detailed example of how to convert a recurring decimal to a fraction, a common topic in Recurring Decimals GCSE questions and answers. The process is broken down into six clear steps, making it an excellent resource for students working on recurring decimals to fractions worksheets.

The example used is 0.738̅, which is a recurring decimal where the 8 repeats indefinitely. The method shown can be applied to various recurring decimals to fractions examples, making it a versatile technique for GCSE maths.

Definition: A recurring decimal is a decimal number where a digit or group of digits repeats indefinitely after the decimal point.

Step 1 involves setting the recurring decimal equal to a variable x. This is the foundation for the algebraic approach used in this method.

Example: Let x = 0.738̅

Step 2 requires multiplying both sides of the equation by 10 for each non-recurring decimal place. In this case, there are two non-recurring decimal places (7 and 3), so we multiply by 10.

Highlight: 10x = 7.38̅

Step 3 involves multiplying both sides by 10 for each recurring decimal place. Here, only the 8 is recurring, so we multiply by 100.

Example: 1000x = 738.38̅

Step 4 is crucial as it involves subtracting the equations from steps 2 and 3. This clever step cancels out the recurring part of the decimal.

Highlight: 1000x - 10x = 738.38̅ - 7.38̅

Step 5 solves for x by simplifying the equation from step 4.

Example: 990x = 731

Step 6, the final step, involves simplifying the fraction if possible. In this case, the fraction 731/990 is already in its simplest form.

Vocabulary: Simplest form means that the numerator and denominator have no common factors other than 1.

This method can be applied to various recurring decimals to fractions questions, making it an essential skill for GCSE maths. Students can practice with a recurring decimals to fractions worksheet or use a recurring decimals to fractions calculator to check their work.