Question

Converting repeating decimals to fractions 3.83333333

Answer 1

Let $u=3.8\bar{3}$, then $10u=38.\bar{3}$ and $100u=383.\bar{3}$

That means $90u=100u-10u=383.\bar{3}-38.\bar{3}=345$.

Solving for $u$ gives us a fraction $u=\frac{345}{90}=\boxed{\frac{23}{6}}=3.8\bar{3}$.

Hope this helps.