Question

Express the following as a non-terminating recurring decimal.

$\frac{13}{44}$

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 $\frac{13}{44}$.

$440.295454130\underline{-88}420\underline{-396}240\underline{-220}200\underline{-176}240\underline{-220}200\underline{-176}24$

Thus, $\frac{13}{44}=0.295454...=0.29\overline{54}$.

Therefore the given number is non-terminating recurring decimal.