Question

Express the following as a non-terminating recurring decimal.

$\frac{1}{15}$

Answer 1

Terminating decimals:

$\frac{p}{q}$is terminating if

1. p and q are co-prime
2. q is of the form $2^n$$5^m$, where n and m are non-negative integers.

Non-terminating decimals:

The rational numbers which can not be expressed as terminating decimals.

Ex. $\frac{2}{3},\frac{5}{11},...$

Given number is $\frac{1}{15}$.

$150.0666100\underline{-90}100\underline{-90}100\underline{-90}10$

Thus, $\frac{1}{15}=0.0\overline{6}$.

Therefore the given number is a non-terminating recurring decimal.