[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]
