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Terminating decimal

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Terminating decimal

by sureng » Wed Apr 13, 2011 9:26 am
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals. If a, b, c, d and e are non-negative integers and p = 2^a 3^b and q = 2^c 3^d 5^e, is p/q a terminating decimal?

(1) a > c

(2) b > d

NOTE: ^ stands for power

The only way i could solve is by substituting sample values for a,b,c,d. I saw some explanations in other websites(including MGMAT website) but didn't understand the approach at all. Any body found a systematic approach(easy) for this type of problem?
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by manpsingh87 » Wed Apr 13, 2011 9:37 am
sureng wrote:Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals. If a, b, c, d and e are non-negative integers and p = 2^a 3^b and q = 2^c 3^d 5^e, is p/q a terminating decimal?

(1) a > c

(2) b > d

NOTE: ^ stands for power

The only way i could solve is by substituting sample values for a,b,c,d. I saw some explanations in other websites(including MGMAT website) but didn't understand the approach at all. Any body found a systematic approach(easy) for this type of problem?
any number when divided by 2 or 5(or both) will result in a terminating number..

now consider the question..!!
p = 2^a 3^b;
q = 2^c 3^d 5^e; now for p/q to be a terminating, we must have denominator in powers of 2 and 5 only.

now consider 1)a>c, i.e. denominator won't contain any power of 2, also we must have denominator in power of 2 and 5 only, as nothing is mentioned about the power of 3 i.e. b,d so 1 alone is not sufficient to answer the question.

2) b>d, i.e. denominator would be free from 3, i.e. it will contain only powers of 2 and 5, hence p/q would result in a terminating number. hence B
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by rohu27 » Wed Apr 13, 2011 9:42 am
It can be solved easily if you really understand the concept of terminating decimals.
for ex: 1/2=.5 is a terminatign decimal, 1/3=.33333 it goes on forever, so non terminating. similarly 1/4,1/5 are terminating.

now the Q asks, p/q=2^a 3^b/2^c 3^d 5^e
here the only thing which shud worry you is the power of 3. whatevr the power of 2 or 5 it will always terminate. it all depends on 3. if b>d we have something like 3^b-d so it will be terminating, if b<d we have 1/3^b-d which is not terminating.

look at the statements now, 1 is not suff as we are not bothered abt powers of 2
b gives us info abt 3's powers. so b is suff.

hope tht helps.
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