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What is 0.3111111111111111 as a fraction?

Sagot :

iGreen
[tex]\sf~N=0.3\overline{1}[/tex]

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

[tex]\sf10N=3.\overline{1}[/tex]

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

So we have:

[tex]\sf9N=2.8[/tex]

Divide 9 to both sides:

[tex]\sf~N=\dfrac{2.8}{9}[/tex]

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

[tex]\sf~N=\dfrac{28}{90}[/tex]

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

[tex]\sf~N=\boxed{\sf\dfrac{14}{45}}[/tex]
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