Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:


(i)



(ii)



(iii)



(iv)



(v)



(vi)



(vii)



(viii)



(ix)



(x)





(i)


Factorize the denominator we get,


3125 = 5×5×5×5×5 = 55


The denominator is of the form 5m


Hence, the decimal expansion of is terminating.


(ii)


Factorize the denominator we get,


8 = 2 × 2 ×2 = 23


The denominator is of the form 2m


Hence, the decimal expansion of is terminating.


(iii)


Factorize the denominator we get,


455 = 5×7×13


Since, the denominator is not in the form of 2m × 5n, and it also contains 7 and 13 as its factors,


Its decimal expansion will be non-terminating repeating.


(iv)


Factorize the denominator we get,


1600 = 26×52


The denominator is in the form 2m × 5n


Hence, the decimal expansion of is terminating.


(v)


Factorize the denominator we get,


343 = 73


Since the denominator is not in the form of 2m × 5n, it has 7 as its factors.


So, the decimal expansion of non-terminating repeating.


(vi)


The denominator is in the form 2m×5n


Hence, the decimal expansion of is terminating.


(vii)


Since, the denominator is not in the form of 2m × 5n, as it has 7 in denominator.


So, the decimal expansion of is non-terminating repeating.


(viii)


The denominator is in the form 5n


Hence, the decimal expansion of is terminating.


(ix)


Factorize the denominator we get,


10 = 2×5


The denominator is in the form 2m×5n


Hence, the decimal expansion of is terminating.


(x)


Factorize the denominator we get,


30 = 2×3×5


Since the denominator is not in the form of 2m × 5n, as it has 3 in denominator.


So, the decimal expansion of non-terminating repeating.


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