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terminating decimal

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terminating decimal

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If a, b, c, d and e are 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

OA B

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jainrahul1985 wrote:
If a, b, c, d and e are 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

OA B
Dividing by a power of 2 results in a terminating decimal:
1/2 = .5
1/2² = .25
1/2³ = .125
etc.

Dividing by a power of 5 results in a terminating decimal:
1/5 = .2
1/5² = .04
1/5³ = .008
etc.

Dividing by a power of 3 results in a non-terminating decimal:
1/3 = .33333...
1/3² = .11111...
1/3³ = .037037037...

Thus, we need to know whether (2^a * 3^b) / (2^c * 3^d * 5^e) will require dividing by a power of 3.
If there are more 3's in the denominator than in the numerator, then (2^a * 3^b) / (2^c * 3^d * 5^e) will require dividing by a power of 3.
Since the number of 3's depends on the sizes of the exponents, the question can be rephrased:

Is b>d?

Statement 1: a>c.
No way to know whether b>d.
Insufficient.

Statement 2: b>d.
Sufficient.

The correct answer is B.

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Also, its helpful to know that in a fraction (a/b) if b were to have any prime factor other than 2 or 5 it would be a non-terminating decimal.

Here, any powers of 2 and 5 would give you a terminating decimal, we are only concerned about powers of 3. If you know b>d, the denominator would not have a 3, so we can say for sure for any values of a,c and e, the fraction would be a terminating fraction

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