Question

12/625,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:
12/625
13 / (5⁴)
Here, the factors of the denominator 625 are are 5⁴ which is in the form 2ⁿ 5^m .
Hence , 12/625 has terminating decimal expansion and can be expressed as
12/625 = 12 × 2⁴ / (5⁴ × 2⁴)
= 12 × 16 / (2×5)⁴ = 192 /10000
= 0.0192

Hence, the decimal expansion of 12/625 = 0.0192

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

12/625

= 12/5⁴

Here ,

Denominator ( q ) = 5⁴ , which is of the

form 2^n × 5^m ( n = 0 and m = 4 ) .

So , the rational number 12/625 has

a terminating decimal expansion .

12/625

= 12/5⁴

= ( 12 × 2⁴ )/( 2⁴ × 5⁴ )

= 192/( 10⁴ )

= 0.0192

( terminating decimal )

I hope this helps you.

: )