Question

How do we represent $13.\overline{56}$?

• A. $\frac{123}{990}$
• B. $\frac{1343}{990}$
• C. $\frac{1343}{99}$
• D. $\frac{1143}{99}$

Answer 1

The correct option is C $\frac{1343}{99}$

Let $x=13.\overline{56}$
$x=13.565656$...........(i)
Here the number of repeating digits is two.
So multiply both sides of (i) by 100, we get
$100x=1356.565656$.............(ii)
Subtracting (i) from (ii), we get
$99x=1343.0$
$x=\frac{1343}{99}$
Hence, $13.\overline{56}=\frac{1343}{99}$