Question

Calculate whether the following rational numbers will have terminating or non terminating decimal expansion.
(i)
$\frac{13}{2125}$
(ii)
$\frac{23}{ {2}^{3} \times {5}^{2} }$
(iii)
$\frac{129}{ {2}^{3} \times 5 \times {1}^{3} }$
Please provide good answer and I will mark you brainliest. Calculate !!!
​

Answer 1

Answer:

Step-by-step explanation:

(i)13/2125

denominator=2125= 5*5*5*7

denominator is not of the form 2^n*5^m since it has 17 as a factor

hence it will have non-terminating decimal expansion

(ii)23/2³*5²

the denominator is of the form 2^n*5^m

hence it will have terminating decimal expansion

(iii)129/2³*5*1³

denominator= 2³*5*1³ = 2³*5¹

the denominator is of the form 2^n*5^m

hence it will have terminating decimal expansion