\(\sf~N=0.3\overline{1}\)
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:
\(\sf~N=\boxed{\sf\dfrac{14}{45}}\)
