# 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

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.*Recurring (sometimes also called repeating)*–

TheWendyBird says

Thank you! Ugh my exam is tomorrow so I am cramming – I have a feeling I am

going to be using your videos quite a lot today :’) Thank you so much, you

explain things very quickly and simply.

matt selwob says

Thanks

leah38521 says

This was a really helpful video thankyou for uploading it

rove lopez says

thank you so much for you help i was so straggle with it but now i know

how to do

Jake Joyce says

Thank you 🙂

Simon Deacon says

That’s great and thanks for letting me know – all best S

Emma Balmer says

This is great!! Thank you so much! Brilliant!!

Simon Deacon says

Hi – no, it’s usually non calculator. Rgds S

Ali Abokar says

is this for the calculator paper?

Vay Skabrin says

you’re sooo helpful thanks so much !!

Misznovember says

thanks 🙂 i was stuck on that exact question! (the last one)