Question

without actual division find which of the following rational numbers are terminating decimals 9/7, 283/16

Answer 1

Solution:

To find : the fractions that are terminating

We know that if a fraction terminates its denominator factorization is in the form of 2^m*5^n

So by using it let us factorise the denominators of the two fractions.

9/7 => 7 = 1*7

Thus the prime factorization of it is not in the form of 2^m*5^n

Hence it will not terminate.

283/16

=> 16 = 2*2*2*2 = 2^4

Thus, 16 = 2^4*5^1

This signifies that the prime factorization of the denominator is in the form of 2^m*5^n.

Hence the fraction 283/16 will terminate.