Question

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

Answer 1

Let x = 1.6666...... ----- (i)
then, 10x = 16.666666 ----- (ii)

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