Question

Without performing division check whether the following rational numbers will have a terminating decimal from or none-terminating repeating decimal form.(RP)
i) $\frac{11}{12}$

ii) $\frac{15}{1600}$

Answer 1

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

a) p and q are co-primes

and

b) q is of the form $2^m\times 5^n$ ,where m and n are non negative integers

i) $\frac{11}{12}$

$11$ and $12$ have no common factors ,so $11$ and $12$ are co-primes

$12=$ $2^2\times 3^1$

Denominator $12$ is not of the form $2^m\times 5^n$

Hence $\frac{11}{12}$ is a non-terminating repeating decimal

ii) $\frac{15}{1600}$$=\frac{3}{320}$

Here, $3$ and $320$ have no common factors ,so $3$ and $320$ are co-primes

$320=$$2^6\times 5^1$

Denominator $320$ is of the form $2^m\times 5^n$ where, $m=6$ and $n=1$where, m and n are non negative integers

Hence $\frac{15}{1600}$ is a terminating decimal