Roman C. answered • 01/30/13

Masters of Education Graduate with Mathematics Expertise

For terminating decimals, just multiply and divide by 10^{n} 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...

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999*X = 1518.75

99900*X = 151875

X = 151875/99900 = 225/148

You can check this using a calculator.