Question

When the repeating decimal $10.363636$ is written in simplest functional form $\frac{p}{q}$, find the value of $p+q$

Answer 1

Consider,

$x=10.363636$ (1)

Multiply both sides of equation (1) by 100.

$100x=100\times 10.363636$

$100x=1036.363636$ (2)

Subtract equation (2) from equation (1).

$99x=1026$

$x=\frac{1026}{99}$

$x=\frac{114}{11}$

This gives that $p=114$ and $q=11$

$p+q=114+11$

$p+q=125$