What does it mean when it says a number is recurring?

By Gareth Banks on the 6th of March, 2013

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    Recurring decimals refer to decimals where numbers continuously repeat themselves indefinitely. Sometimes its just a single number that is recurring and other times it can be a sequence of numbers. This is shown by placing a dot above the repeated number(s). The most common example of this is the decimal value for a third, which is 0.3 recurring (appologies I don't seem to be able to show the sign, which in this instance would be a solid dot above the three).

    Refine By Ellie Beecham on the 6th of March, 2013

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Identify recurring and terminating decimals

There are three types of decimal numbers:

Terminating, Recurring and Non-recurring

Terminating decimals stop at some point. 1.5 is an example of a terminating decimal. So is 4.75, and 0.33265985. No matter how many decimal places there are, provided it stops, it is a terminating decimal.

Recurring decimals repeat forever, but there is a pattern to their repetition. These are presented either by dots after the number, showing that it continues, or using proper mathematical notation, a dot above the number that repeats.

E.g. Put 1/3 into a calculator, and it will either show 0.33333333333… or 0.3 ̇, depending on the calculator type. If a pattern of numbers repeats, rather than just a single number, then two dots show where the repeating pattern begins and ends, e.g. 1/7 = 0.1 ̇42857 ̇ = 0.142857142857142857…

Non-recurring decimals are decimals that go on forever, but there is no pattern. These are also called ‘irrational’ numbers. Examples include π and √2.

There are some tricks for spotting whether a fraction will result in a recurring or terminating decimal:

If the denominator has prime factors of only 2 or 5, the result will be a terminating decimal e.g. 1/25 = 0.04

If the denominator does not have 2 or 5 as a prime factor, the result will be a recurring decimal e.g. 1/7 = 0.1 ̇42857 ̇

If the denominator has prime factors of either 2 or 5, and other prime factors as well, then the result will be a recurring decimal with a section at the start that doesn’t repeat e.g. 1/22 = 0.04 ̇5 ̇

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