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# How do I convert a decimal to a fraction?

By Gareth Banks on the 6th of March, 2013

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So decimals, fractions and percentages are all similar, they are ways of expressing proportion. They are all closely related and completely interchangable with each other.

To convert a decimal into a fraction you need to look at the number of decimal points first, this determines the bottom number of the fraction. So if there are 2 decimal places then the bottom number will be 100, 3 decimal places and the bottom number would be 1000, and so on. The top number is then the number shown in the decimal ....I guess this is best explained in an example:

0.6 = 6/10, 0.06 = 6/100, 0.006 = 6/1000

0.32 = 32/100,  0.032 = 32/1000, 0.302 = 302/1000

These can then be cancelled down further to make less complicated fractions.

By Ellie Beecham on the 6th of March, 2013

## Convert between decimals, fractions and percentages

The one word that could describe all these three is PROPORTIONDecimals, fractions and percentages are simply three different ways of expressing a proportion of something. Its important that you see them as closely related to one another and are completely interchangeable with each other.

This table shows the common conversions which you should be able to know without having to work them out each time:

For those that you don't know there are some simple methods for converting between the three types.

## The Awkward One - Decimals to Fractions

Converting decimals to fractions is fairly straight forward when you have exact (terminating) decimalsIt's probably best illustrated by examples, hopefully from these you should be able to work out the rule...

(Just remember to simplify them down where you can)

## Recurring Decimals into Fractions

Even the scary looking recurring decimals like 0.33333... are actually just exact fractions in disguise. There are two ways to tackle these:

1) by UNDERSTANDING

2) by just LEARNING THE RESULT

Understanding

1. Find the length of the repeating sequence and multiply by 10, 100, 1000, .... or whatever to move it all up past the decimal point by one full repeated lump. e.g. 0.231234234... x 1000 = 234.234234...
2. Subtract the original number, r, from the new one (which in this case is 1000r). i.e. 1000r - r = 234.234234... - 0.234234... giving:  999r = 234
3. Then just DIVIDE to leave r:

Learning The Result

The fraction always has the repeating unit on the top and the same number of nines on the bottom, its as easy as that!

(Again, remember to simplify them down where you can)

## Follow the links below to see how this topic has appeared in past exam papers

AQA Unit 2 March 2011 (F) - Page 5, Question 7

AQA Unit 2 June 2011 (H) - Page 3, Question 3

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