Recurring decimal

Definition

A decimal in which a digit or block of digits repeats for ever, such as $0.\overline{27}=0.272727\ldots$ .

Used by AQA, Edexcel and OCR

Specification N10 · Paper 1, Paper 2, Paper 3

A recurring decimal is exact: the dots do not mean that the value has merely been rounded.
Revise: Fractions and Decimals Conversion

Specification N10 · Paper 1, Paper 2, Paper 3

A decimal in which a digit or block of digits repeats for ever, such as $0.333$ or .

1
For a recurring decimal, multiply by a power of 10 that places identical recurring tails underneath one another before subtracting.
2
When converting a recurring decimal to a fraction, define the decimal with a letter, multiply by a suitable power of 10, and show the subtraction explicitly.
3
Give an exact, fully simplified fraction. Do not round the recurring decimal.

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0.333 \dots

0.4545\ldots

A recurring decimal has a digit or block of digits that repeats for ever.

Specification 2.02a · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)

A decimal whose digit or block of digits repeats indefinitely after the decimal point.
A recurring decimal contains a digit or block of digits that repeats for ever.
Revise: Converting Recurring Decimals and Fractions