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=(345)/(90)=\boxed{(23)/(6)}=3.8\bar{3}`.

Hope this helps.