1.2.13

Convert Recurring Decimals

Test yourself

Converting Recurring Decimals to Fractions

To convert a recurring decimal into a fraction e.g. 0.2545454545454... do the following things:

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Step 1

  • Name the decimal.
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Step 2

  • Multiply by a power of ten to move any non repeating parts of the number to the left of the decimal point.
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Step 3

  • Expand the decimal by one repeating section.
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Step 4

  • Multiply by a power of ten so that one repeating section is to the left of the decimal point but the recurring section is to the right.
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Step 5

  • Subtract one from the other to remove the recurring part of the number.
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Step 6

  • Divide to leave r on its own on one side then cancel if possible.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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