Question

14/15625,State whether given rational number have terminating decimal expansion or not and if it has terminating decimal expansion, find it.

Answer 1

If the factors of denominator of the given rational number is of form 2ⁿ 5^m ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.

SOLUTION:
14/15625
14 / (5^6)
Here, the factors of the denominator 15625 are are 5^6 which is in the form 2ⁿ 5^m . It has terminating decimal expansion and can be expressed as
14/15625 = 14 × 2^6 / (2^6 × 5^6)
= 14 × 64/ (2×5)^6 = 896/1000000
= 0.000896

Hence, the decimal expansion of 14/15625 = 0.000896

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Dear Student,

To check whether given number is terminating decimal expansion or not.

Do prime factors of denominator,it they are in the form if
${2}^{n} \times {5}^{m}$
where n ,m = 0,1,2,3...

$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \\ \\ = {5}^{6}$
so,denominator is in the form of
${2}^{0} \times {5}^{6}$
given number 14/15625 is terminating decimal expansion.
it is 0.000896

Hope it helps you.