How do you turn 0.11111... (recurring) into a fraction

Let's look at what makes this question more difficult than, say, 0.5 or 0.01: as the decimal is recurring, you can't just multiply and divide by a big number to get a fraction. Example: multiply 0.01 times 100, then divide by 100. You get 1/100 which is your fraction. However, if you multiply 0.11111... by 100 you get 11.11111... (still recurring). This just means we require an additional step to solve this. Let's try to get rid of the recurring decimal with some simple operations: let x = 0.111111... then 10x = 1.111111... 10x - x = 1.111111... - 0.111111... = 1 and: 10x - x = 9x So, we can write 9x = 1. Hence, x = 1/9 is your fraction. We can expand this method for all sorts of recurring decimals, like 0.12121212... or 0.426426426... with slight changes in our method, which I would like you to try and find, (Hint: remember we want to get rid of the recurring decimal).

AP
Answered by Alvaro P. Maths tutor

49494 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations y = 5x^2 + 4x - 19 and y = 4x + 1


The exchange rate between dollars and euros(€) is €1 = $1.158 . (a) Felicity changes €4900 into dollars. Work out how many dollars she receives.


Expand and Simplify: (x+2)(x+3)(x−3)


x – 7x + 10 = 0


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning