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Change decimals to fractions and vice versa

most common conversions you should know

1/2 0.5 50%

1/4 0.25 25%

3/4 0.75 75%

1/3 0.333333... 33 1/3%

2/3 0.666666... 66 2/3%

1/10 0.1 10%

2/10 0.2 20%

1/5 0.2 20%

2/5 0.4 40%

Conversion from fraction to decimal

Fraction > divide e.g. 7/20 is 7 divided by 20 > decimal e.g. =0.35

Conversion from decimal to fraction

decimal > fraction

Terminating decimals to fractions - the digits after the decimal point go on the top and a power of 10 on the bottom - with the same number of zeros as there were decimal places.

0.6 = 6/10

0.12 = 12/100

0.345 = 345/1000

recurring decimals to fractions

write 0.234234234... as a fraction

1) name your decimal - I've called it r

let r = 0.234234234...

2) multiply r by a power of ten to move it past the decimal point by one full repeated lump - here that's 1000:

1000r = 234.234234234...

3) now you can subtract to get rid of the decimal part:

1000r =234.234234234...

- r = 0.234234234...

999r = 234

then just divide to leave r, and cancel if possible

r = 234/999 = 26/111

write 0.16666... as a fraction

1) name your decimal

let r = 0.16666...

2) now multiply r by a power of ten to move the non-repeating part past the decimal point.

10r = 1.6666...

3) now multiply again to move one full repeated lump past the decimal point

100r = 16.66666...

4) subtract to get rid of the decimal point

100r = 16.6666...

- 10r = 1.6666

90r = 15

5) Divide to leave r and cancel if possible

r = 15/90 = 1/6