Question

Calculate the difference between $1.8$ and $1.\overline{08}$.
(Note: A bar indicates a digit pattern that is repeated)

• A. $0.7\overline{1}$
• B. $0.\overline{71}$
• C. $0.7\overline{19}$
• D. $0.7\overline{2}$
• E. $0.\overline{72}$

Answer 1

Answer: (C)

$0.7\overline{19}$

Let $x=1.\overline{08}$

Now, $100x=108.\overline{08}$

$\Rightarrow 100x=107+1.\overline{08}$

$\Rightarrow 100x=107+x$

$\Rightarrow x=\frac{107}{99}$
$\Rightarrow 1.\overline{08}=\frac{107}{99}$

Now $1.8$ is equivalent to $\frac{9}{5}$
Hence $1.8-1.\overline{08}=\frac{9}{5}-\frac{107}{99}$

$=\frac{891-535}{495}$

$=\frac{356}{495}$

$=0.7\overline{19}$