# Maths unit B:Convert fractions to recurring decimals and represent recurring decimals as fractions

• Created by: rvsn
• Created on: 25-11-14 19:28

## Converting a fraction to a recurring decimal

-Divide it as normal

-Once you find a pattern then you can place the dots above the number to show the repeats

-If one number is repeated then the dot would just go above the number e.g. 0.3 would have the dot above 3

-If two numbers are repeated the dot would go above each number e.g.0.73 would have the dot above the 7 and the 3

-If a series of numbers are repeated the dot would go above the first and last number of that pattern e.g. 0.47829 would have the dot above the 4 and the 9

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## Representing a recurring decimal as a fraction

-define the decimal as x

-Multiply x by a multiple of 10 so that the recurring number(s) is(are) also a whole number on the other side of the point, make the decimals match

-Take x'saway from each other so you get an integer

-Solve the equation so you have x alone

e.g.(1) Represent 0.555...recurring as a fraction: x=0.5555...  10x= 5.5555.. 10x-x=5 9x=5 x=5/9

e.g.(2)Represent 0.457457..recurring as a fraction x=0.457457... 1000x=457.457457... 1000x-x=457 999x=457 x=457/999

e.g.(3) Represent 0.32222...recurring as a fraction x=0.3222... 10x=3.222... 100x=32.2222...(to make the decimals match up) 100x-10x=29 90x=29 x=29/90

e.g.(4) Represent 0.4575757...recurring as a fraction x=0.4575757.. 10x=4.5757.. 1000x=457.5757 1000x-10x=453 990x=453 =453/990=151/330

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