Express 0.545454... as a fraction in its simplest form.

First, we are going to give our decimal a name, let's call it x. We notice that x repeats after two digits, so how about we look at 100x.

100x = 54.54545454...

But, the decimal part of this number is what we called x, so let's subtract it.

100x - x = 54.5454545454... - 0.54545454

Working out both sides, we get

99x = 54

So, x = 54/99. However, we are not finished as the question said "in its simplest form". Either notice that 99 and 54 are both divisible by 9, or that they're divisible by 3 twice and we get the final answer.

x = 6/11

Answered by Felix S. Maths tutor

29422 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Find the two points of intersection of the graphs 2x+y=7 and x^2-8x+7=y. Solve using only algebraic methods (no graphical).


n is an integer greater than 1. Prove algebraically that n^2-2-(n-2)^2 is always an even number


How do you add fractions? And how do you multiply fractions?


Factorise fully x^2+6x+5=0


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