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# Change decimal to fraction

For terminating decimals, just multiply and divide by 10n where n is the number of digits, and then reduce the fraction. For instance with 0.28, we have

0.28 = 0.28 * 100 / 100 = 28 / 100 = (4*7) / (4*25) = 7/25

For repeating decimals, you can reduce the problem to the case of terminating decimal with a little algebra. And then apply the method above. Let's do this with 1.52027027027027...

1000*X = 1520.27027027027027...

X =      1.52027027027027...

--------------------------------------------

999*X   = 1518.75

99900*X = 151875

X = 151875/99900 = 225/148

You can check this using a calculator.

Tried to post an answer to this earlier but it won't load so apologies if this ends up as a double response.

Decimals are ratios of the number to a corresponding power of ten.

0.1 = 1/10

0.25 = 25/100 simplified to (25*1)/(25*4) = 1/4

0.44 = 44/100 simplified to (4*11)/(4*25) = 11/25

0.3125 = 3125/10000 simplified to (625*5)/(625*16) = 5/16

If the decimal has a number greater than one then just multiply it by the same power of ten you divide by (according to the number of decimal places) and make that the numerator.

2.5 = (2.5*10)/10 = 25/10 simplifies to (5*5)/(5*2) = 5/2

3.72 = (3.72*100)/100 = 372/100 and simplifies to (93*4)/(25*4) = 93/25

Remember the series:

1/10 is one tenth = 0.1

1/100 is one hundredth = 0.01

1/1000 is one thousandth = 0.001

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