Find the decimal expansions of $\frac{10}{3}$,$\frac{7}{8}$ and $\frac{1}{7}$.

(N/A) For $\frac{10}{3} = 3.333... = 3.\overline{3}$. The remainder is always $1$,which repeats. The divisor is $3$.
For $\frac{7}{8} = 0.875$. The remainder becomes $0$ after a finite number of steps. The divisor is $8$.
For $\frac{1}{7} = 0.\overline{142857}$. The remainders are $3, 2, 6, 4, 5, 1$ which repeat. The divisor is $7$.
Observations:
$(i)$ The remainders either become $0$ after a certain stage,or start repeating themselves.
$(ii)$ The number of entries in the repeating string of remainders is less than the divisor.
$(iii)$ If the remainders repeat,then we get a repeating block of digits in the quotient.