Question

What is 0.3111111111111111 as a fraction?

Answer 1

$\sf~N=0.3\overline{1}$

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:

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