Finite number of non-zero digits

[mehravikas]

Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?

(1) P>Q
(2) Q=8

OA is: E

[raju232007]

This question has already been posted in this forum..Kindly use the search thread before posting questions

Well,consider this

To find whether a fraction is terminating or not
1.Prime factorize the denominator
2.If there is a prime factor besides 2 or 5 in the denominator,the fraction represents a recurring decimal..

As per statement 2
q=8..and it contains only prime factor 2

Hence this information is sufficient to prove that the given fraction contains only a finite number of non zero digits...

Hence the ans should be B and not E...Hope this helps

[Ian Stewart]

To find whether a fraction is terminating or not
1.Prime factorize the denominator
2.If there is a prime factor besides 2 or 5 in the denominator,the fraction represents a recurring decimal..

You need to add one step here, at the beginning:

1. Reduce your fraction completely

Otherwise, according to your test, 3/30 should be a recurring decimal; it's not, because it reduces to 1/10.

[raju232007]

Yeah..sure..Thanks for your input...

[vineetbatra]

[quote="Ian Stewart
You need to add one step here, at the beginning:

1. Reduce your fraction completely

Otherwise, according to your test, 3/30 should be a recurring decimal; it's not, because it reduces to 1/10.[/quote]

Hello Ian,

I tend to agree with you, P her can be 8 or 16, but can you please explain what do you mean by "Reduce your fraction completely"

Also raju mentioned that "If there is a prime factor besides 2 or 5 in the denominator,the fraction represents a recurring decimal", so in other words if my denominator is 30, then my prime factors are 2,3,5 and 30 will not lead a finite fraction, however if my denominator is 10 then 8, then it will lead a finite factor.

Please explain.

[Ian Stewart]

I tend to agree with you, P her can be 8 or 16, but can you please explain what do you mean by "Reduce your fraction completely"

Also raju mentioned that "If there is a prime factor besides 2 or 5 in the denominator,the fraction represents a recurring decimal", so in other words if my denominator is 30, then my prime factors are 2,3,5 and 30 will not lead a finite fraction, however if my denominator is 10 then 8, then it will lead a finite factor.

Please explain.

By 'reduce your fraction', I mean 'cancel any divisors common to the numerator and denominator'. The fraction 21/30 is not reduced, because we can cancel a 3 from the top and bottom; the fraction is equivalent to 7/10. If you know the denominator of a fraction is 30, you cannot be certain whether its decimal equivalent will terminate, since it may be that the 3 in the denominator cancels with a 3 in the numerator. If it does, the decimal will terminate, and if it does not, the decimal will repeat.