Q. 14.4( 11 Votes )

Write whether the

Answer :

A terminating decimal is a decimal that ends. It must have finite number of digits after the decimal point.

While, a non-terminating decimal is a decimal that continues endlessly. For example: π


Also more theoretically, we can say is a terminating decimal if


(a) p and q are co-primes.


(b) q is of the form 2n5m.


Here, p=7 and q=75.


Checking for co-primes:


Factors of 7 = 1, 7


Factors of 75 = 1, 3, 5, 15, 25, 75


Common factors of 7 and 75 = 1


7 and 75 are co-primes.


[ two numbers are co-primes if the only number that divides them is 1]


And since, 75 = 3 × 5 × 5 ≠ 2n5m


Thus, is non-terminating decimal.


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