Question

1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form.
Then $p+q$ is .

• A. 8
• B. 9
• C. 6

Answer 1

The correct option is A 8

Let $x=\mathrm{1.6666......}$ ----- (i)
then, $10x=16.666666$ ----- (ii)

Subtracting (i) from (ii), we get
$10x-x=\left(\mathrm{16.666666...}\right)-\left(\mathrm{1.666666...}\right)$
$\Rightarrow 9x=15$
Hence, $x=\frac{15}{9}=\frac{\frac{15}{3}}{\frac{9}{3}}=\frac{5}{3}$
i.e., $p=5andq=3$
So, $p+q=8$