How do I identify terminating decimals?

By Lisa Kelly on the 11th of June, 2012

2 Answers

  • 1

    A decimal is a terminating decimal if it stops at some point.

    So any decimal that doesn't go on forever is a terminating decimal.

    Examples of terminating decimals
    1.5, 2.34, -78.1, 1.5824 

    Refine By Lee Mansfield on the 14th of June, 2012

  • 0

    The opposite of this would be something like PI which is an infinite number

    Refine By henry warren on the 10th of August, 2012

Suggested reading…

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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