# Recurring decimals to fractions

Mind Map by , created over 6 years ago

## GCSE Maths (Year 8 Number 2) Mind Map on Recurring decimals to fractions, created by Ellen Billingham on 05/11/2013.

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 Created by Ellen Billingham over 6 years ago
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Recurring decimals to fractions
1 What is 0.454545454545454545(recurring) as a fraction?
1.1 1. Write it as x = 0.4545454545...
1.1.1 2. Multiply the decimal by a power of 10 that leaves the bit after the decimal the same
1.1.1.1 (x100) 100x = 45.454545...
1.1.1.1.1 3. Subtract the original number from the new one
1.1.1.1.1.1 99x = 45.
1.1.1.1.1.1.1 Divide by the number of x
1.1.1.1.1.1.1.1 45 ÷ 99 = 45/99
1.1.1.1.1.1.1.1.1 Cancel the fraction
1.1.1.1.1.1.1.1.1.1 5/11
2 0.238383838...
2.1 x = 0.238383838
2.1.1 You can't get it so that the number is the same on both sides because of the 2.
2.1.2 1000x = 238.3838383838
2.1.2.1 10x = 2.38383838
2.1.2.1.1 990x = 236
2.1.2.1.1.1 x = 236/990
2.1.2.1.1.1.1 118/445