# Without actual division, find which of the following rational numbers have terminating decimal expansion. (i) 7/128 (ii) 21/15 (iii) 219/2200

668 views

closed

Without actual division, find which of the following rational numbers have terminating decimal expansion.

(i) $\frac{7}{128}$

(ii) $\frac{21}{15}$

(iii) $\frac{219}{2200}$

+1 vote
by (48.7k points)
selected by

(i) $\frac{7}{128}$

So $\frac{7}{128}$ = $\frac{7}{2^75^0}$

This of the form 4m, n ∈ W

So $\frac{7}{128}$ has a terminating decimal expansion

(ii) $\frac{21}{15}$

So $\frac{21}{15}$ has a terminating decimal expansion.

(iii) $\frac{219}{2200}$

$\frac{219}{2200}$ = $\frac{219}{2^35^211^1}$

∴ This is not of the form $\frac{p}{2^m5^n}$

So $\frac{219}{2200}$ has a non-terminating recurring decimal expansion.