Question

47/500,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:
47/500
47 / (2²× 5³)
Here, the factors of the denominator 500 are 2² × 5³ which is in the form 2ⁿ 5^m .It has a terminating decimal expansion.
47/500 = 47 × 2¹/ (2¹ × 2²× 5³)
= 94/ (2³ 5³) = 94/10³ = 94/1000 = 0.094
Hence ,the decimal expansion of 47/500 94/1000 = 0.094

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

47/500

= 47/( 2² × 5³ )

Here , q = 2² × 5³ , which is of the

form 2^n × 5^m ( n = 2 , m = 3 ).

So , the rational number 47/500

has a terminating decimal .

I hope this helps you.

: )