Question

without long division check whether the decimal expension

(i)
$\frac{173}{2000}$
(ii)
$\frac{173}{2000}$
(iii)
$\frac{1375}{15625}$
​

Answer 1

The decimal representation of rational numbers are terminating if its denominator can be factorized in the form of 2^m × 5^, where m and n are whole numbers.

$\sf \: (i) \: \dfrac{173}{2000} = \dfrac{173}{ {2}^{4} \times {5}^{3} } \bf\implies \:its \: terminating$

$\sf \: (ii) \: \dfrac{173}{2000} = \dfrac{173}{ {2}^{4} \times {5}^{3} } \bf\implies \:its \: terminating$

$\sf \: (iii) \: \dfrac{1375}{15625} = \dfrac{11}{125} = \dfrac{11}{ {2}^{0} \times {5}^{3} } \bf\implies \:its \: terminating$