Question

Decimal expansion of 23/2³5² will terminate or not? if it terminates after how many digits and what is it​

Answer 1

we have to check decimal expansion of 23/2³5² will terminate or not. if it terminates then after how many digits and also what is it.

expression 23/2³5²

we know product of 2 and 5 equals to 10.

denominator of given expression is 2³5². to make it multiple of 10, we have to multiply with 5. it can be done when we multiply and divide by 5.

i.e., 23/(2³5²) × 5/5

= (23 × 5)/(2³5³)

= (115)/(10³)

= 115/1000

= 0.115

it is clear that decimal expansion of 23/2³5² will terminate and it terminates after three digits and it is 0.115.