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Expressing Decimals as Rational Numbers

Express 2.543...

Question

Express 2.5434343..... In the form of p/q where p and q are integers and q is not equal to zero.

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Solution

X=2.5434343....

10x=25.434343......... .eq. 1
1000x=2543.434343.... eq. 2
eq2-eq1

1000x=2543.434343...
10x=25.434343......
990x=2518
x=2518/990

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