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Division of Decimals by Powers of 10

Express 0.254...

Question

Express 0.2545454.............. as a fraction in simplest form.

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Solution

x=0.2545454.....
10x=2.54545454.....
10x=2+0.545454......
10x=2+54/99
10x=(198+54)/99
10x=252/99
x=252/990

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