x = 0.436363636... (recurring). Prove algebraically that x can be written as 24/55.

We need to multiply x by powers of 10 in order to get the recurring part on its own after the decimal point, and then be able to eliminate it. 10x = 4.363636... and 1000x = 436.363636...So subtracting we get 1000x - 10x = 436.363636... - 4.363636...so 990x = 432.Then dividing both sides by 990, we get x = 432/990.We now just need to simplify this fraction: x = 432/990 = 216/495 = 72/165 = 24/55.So we have x = 24/55.


JP
Answered by Joanna P. Maths tutor

25678 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Rana sells 192 cakes in the ratio small : medium : large = 7 : 6 : 11. medium cakes are worth double small ones and large cakes triple small ones. If the cakes go for £532.48 how much is a small cake worth


In a sale, the original price of a bag was reduced by 1/5. The sale price of the bag is £29.40. Work out the original price.


Make y the subject of (y/x)+(2y/(x+4))=3


If m=a^x, n=a^y, and a^2 =(m^y n^x)^z Show xyz=1.


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