The simplest form of $1.\overline{6}$  is

Given is a recuring decimal, $1.\overline{6}$ .
To express it in the form of $\frac{p}{q}$ , assume this number as, say x, and write in the expanded form as follows,
$x=1\cdot \mathrm{66666.......}$                          ……….. (i)
We shift the decimal by 1 place towards the right by multiplying each side of equation (1) by 10 as follows,
$10x=16\cdot \mathrm{66666.....}$                  …………. (ii)
Now, subtract equation (i) from (ii) and simplify as follows,
$\begin{array}{c}10x-x=\mathrm{16.66666.....}-\mathrm{1.66666.....} \\ 9x=15 \\ x=\frac{15}{9}\\ x=\frac{5}{3}\end{array}$ 
From the above result, we can conclude that,
$1.\overline{6}=\frac{5}{3}$ .
Hence, the correct option is (3).