Question

987/10500 will have

(A) Terminating decimal expansion

(B) Non-Terminating Non repeating decimal expansion

(C) Non-Terminating repeating decimal expansion

(D) None of these​

Answer 1

QUESTION -

987/10500 will have

(A) Terminating decimal expansion

(B) Non-Terminating Non repeating decimal expansion

(C) Non-Terminating repeating decimal expansion

(D) None of these

ANSWER -

In any rational number p/q, if q is of the form 2^m5^n, then we can say that the no. is terminating.

In this case, first we find that 987 is divisible by both 7 and 3.

So, divide both numerator and denominator by 7*3.

Thus, we get

47/500

Now we prime factorise the denominator 500.

500=5*5*5*2*2

=5322

which is in the form 2^m5^n.

Hence, 987/10500 is terminating.

@HarshPratapSingh

Answer 2

Hey mate here is your answer ⬇️ ⬇️

If a fraction , in it's lowest terms , has no other prime factors except 2 and 5 it can be expressed as a terminating decimal.

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i ) first write the fraction in it's lowest terms

for that,

Write the numbers into product of prime

and find the HCF of them

987 = 3 × 7 × 47

987 = 3 × 7 × 4710500 = 2 × 2 × 3 × 5 × 5 × 5 × 7

HCF of 987 and 10500 = 3 × 7 = 21

Therefore ,

Least form of the fraction = 987 / 10500

Divide numerator and denominator with HCF,

we get,

= ( 987 / 21 ) / ( 10500 / 21 )

= 47 / 500

987 / 10500 = 47 / 500

Denominator = 500

= 2^2 × 5^2

We have only 2 and 5 as factors .

Therefore ,

987 / 10500 is terminating decimal.