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# How do i divide by a decimal?

By Grainne McLaughlin on the 11th of June, 2012

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When you know how to do long division, figuring out how to divide decimals is easy. However, unlike dividing whole numbers, with decimals, you have to add trailing zeros in the dividend and you also have to complete the problem without remainders.

Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right; at the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right.

For example, suppose you want to divide 10.274 by 0.11. Write the problem as usual:

Turn 0.11 into a whole number by moving the decimal point in 0.11 two places to the right, giving you 11. At the same time, move the decimal point in 10.274 two places to the right, giving you 1,027.4:

By jagadish on the 16th of January, 2013

## 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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