Question

Express $1.\overline{32}+0.\overline{35}$ in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$. Find $p+q$.

Answer 1

We know, $1.\overline{32}=1+0.\overline{32}$

$=x+y$ (lets assume)

$y=0.\overline{32}\Rightarrow 100y=32.\overline{32}$

$=32+0.\overline{32}$ .

$100y=32+y$

$\therefore 99y=32\Rightarrow y=\frac{32}{99}$ .

Similarity, $0.\overline{35}=\frac{35}{99}$ .

$\therefore 1.\overline{32}+0.\overline{35}=(1+\frac{32}{99})+\frac{35}{99}=\frac{99+32+35}{99}=\frac{166}{99}$.

$\therefore \frac{166}{99}=\frac{p}{q}$ and $p+q=166+95=265$.