Question

13/6250,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:
13/6250
13 / (2¹ ×5^5 )
Here, the factors of the denominator 6250 are are 2¹ ×5^5 which is in the form 2ⁿ 5^m .
Hence , 13/6250 has terminating decimal expansion and can be expressed as
13/6250 = 13 × 2⁴ / (2¹×2⁴ × 5^5)
= 13 × 16 / (2×5)^5 = 208 /100000
= 0.00208

Hence, the decimal expansion of 13/6250 = 0.00208

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

13/6250

13/6250 = 13/( 2 × 5^5 )

Here ,

q = 2¹ × 5^5 , which is of the form

2^n × 5^m ( n = 1 and m = 5 ).

So , the rational number 13/6250 has

a terminating decimal .

13/6250

= 13/( 2¹ × 5^5 )

= ( 13 × 2⁴ )/( 2^5 × 5^5 )

= 208/( 10^5 )

= 0.00208 ( terminating decimal )

I hope this helps you.

: )