How do i change a recurring decimal into a fraction?

Let's take 0.666... as an example. In this case we can say x = 0. 666... The next step is to multiply both sides of the equation by 10 so that you end up with 10x = 6.666... Now that we have these 2 equations it is possible to eliminate the recurring part of the decimal as we can subtract x from 10x to end up with 9x = 6. The final part is to divide both sides of the equation such that we have x on its own on the left hand side, leaving us with x = 6/9 which can be simplified to x = 2/3.

GL
Answered by Gail L. Maths tutor

2579 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Paul organised an event for a charity. Each ticket for the event cost £19.95 Paul sold 395 tickets. Paul paid costs of £6000 He gave all money left to the charity. (a) Work out an estimate for the amount of money Paul gave to the charity.


An amount of money was invested for 8 years. It earned compound interest at 2.5% per year. After 8 years the total value of the investment was £11,696.67. Work out the total interest earned.


Make x the subject 2x+3=3x-1


What is the Highest Common Factor of 8 and 24


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences