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