Question

Convert the following:
a) Rational number into decimal form: $\frac{3}{11}$
b) Decimal into rational number: $13.\overline{56}$

Answer 1

Solution:

a) Rational number into decimal form: $\frac{3}{11}$

[2 $\times$ 1 = 2 Mark]
b) Decimal into rational number: $13.\overline{56}$
Let $x=13.\overline{56}$
$x=13.565656$...........(i)
[0.5 Mark]
Here the number of repeating digits is two.
So multiply both sides of (i) by 100, we get
$100x=1356.565656$.............(ii)
[0.5 Mark]
Subtracting (i) from (ii), we get
$99x=1343.0$
$x=\frac{1343}{99}$
Hence, $13.\overline{56}=\frac{1343}{99}$
[1 Mark]