Q. 13.9( 32 Votes )

Without actual division, find which of the following rationals are terminating decimals.

(i) (ii) (iii)

(iv) (v)

Answer :

First we have to know what is terminating decimal. Terminating decimal is the number which has digits that do not go on forever.


(i)


Denominator 80 has factors = 2 × 2 × 2 × 2 × 5


So, 80 has no prime factors other than 2 and 5, thus is terminating decimal.


(ii)


Denominator 24 has factors = 2 × 2 × 2 × 3


So, 24 has factors other than 2 and 5, thus is not a terminating decimal.


(iii)


Denominator 12 has factors = 2 × 2 × 3


So, 12 has factors other than 2 and 5, thus is not a terminating decimal.


(iv)


Denominator 35 has factors = 5 × 7


So, 35 has factors other than 2 and 5, thus is not a terminating decimal.


(v)


Denominator 24 has factors = 5 × 5 × 5


So, 125 has no prime factors other than 2 and 5, thus is a terminating decimal.


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