Repeating decimals to fractions..

.. is a favourite GCSE question, usually grade 7+ and worth around 2/4 marks.

A repeating decimals to fractions question is a little more ‘abstract’ but, once you understand the principles, it should be relatively straightforward. The answer is to use algebra to show a formal proof. As with most mathematics aim for a logical progression with the equals sign in the centre of your working.

The reason for this type of question is that fractions, decimals and percentages can all represent the same information and it’s good to be able to swap between them – particularly for presenting or comparing information.

Actually, any number can be written in “decimal form” and there three different types:

• Exact (sometimes called terminating) – a decimal where you can write down all its digits ie. 16.125. These are the most common types of decimals found in exam questions, apart from…
• Irrational – a decimal that doesn’t repeat such as pi or Euler’s number e (to 50 decimal places 2.71828182845904523536028747135266249775724709369995… try and find the repeats!)

However, there’s another type of decimal form called

• Recurring (sometimes also called repeating) – a decimal which goes on forever and some of the digits are repeated forever i.e. 7.142142142142142… (142 is repeated) Sometimes recurring decimals are written with a bar over the digits which are repeated, or with dots over the first and last digits that are repeated.