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avanturin [10]
3 years ago
9

What is 0.3111111111111111 as a fraction?

Mathematics
1 answer:
Citrus2011 [14]3 years ago
8 0
\sf~N=0.3\overline{1}

There is only one repeating number, so we multiply both sides by \sf10^1 or \sf10.

\sf10N=3.\overline{1}

Now subtract the original number we had to both sides, which is the same as \sf~1N or \sf~N

So we have:

\sf9N=2.8

Divide 9 to both sides:

\sf~N=\dfrac{2.8}{9}

Multiply the fraction by 10 to get rid of the decimal in the numerator.

\sf~N=\dfrac{28}{90}

Simplify the fraction by dividing the numerator and denominator by 2:

\sf~N=\boxed{\sf\dfrac{14}{45}}
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