Question

616/704 is terminating decimal or not (without actual division

Answer 1

Answer :

By prime factorisation of :

616 = 2 × 2 × 2 × 7 × 11

704 = 2 × 2 × 2 × 2 × 2 × 2 × 11

Then,

616/704 =

= (2×2×2×7×11) / (2×2×2×2×2×2×11)

= 7/ (2×2×2)

= 7/8 ...... (1)

We know that, the decimal expansion if terminating if the prime factorisation of the denominator is in the form of 2^m × 5^n , where m and n are non negative integers.

Here in eq. (1) , which is obtained by making the initial fraction in simplest form, the denominator is 8.

On prime factorisation of 8, we get,

8 = 2 × 2 × 2 = 2^3

This can be written as,

8 = 2 × 2 × 2 × 5^0

8 = 2^3 × 5^0 .... (2)

{ we know that any number by the power zero, is equal to 1 }

Here, the denominator is of the form of 2^3 × 5^0 , where 3(m) and 0(n) are non negative integers.

This the denominator of the fraction 7/8 is of the form 2^m × 5^n , where m is 3 and n is 0 respectively.

Thus, the denominator of fraction 616/704 is of the form 2^m × 5^n.

Hence, the fraction 616/704 has terminating decimal expansion.

Answer 2

616/704 is termating decimal or ( with