Recurring decimals to fraction

1. $.\overline{36}=\frac{36}{99}$


2. $2.1\overline{36}=2\frac3{22}$

The part I do not understand however, is "you could used 1) to speed up the working of 2)" which is written in the book.

How would I use 1) to help me work out 2)?

Thanks.

Answer

$$2.1\overline{39}=2+0.1+\frac1{10}\cdot0.\overline{39}$$

So, $$2.1\overline{39}=2+\frac1{10}+\frac1{10}\cdot\frac{36}{99}=2+\frac1{10}\cdot\left(1+\frac4{11}\right)=2+\frac1{10}\cdot\frac{15}{11}=2+\frac3{22}$$