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DS - Decimals and Ratio combined.

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by rajat27 » Wed Feb 20, 2013 10:35 pm
Any decimal that has only a Â…infnite number of nonzero digits is a terminating decimal. For example, 16, 0.73, and 3.178 are three terminating decimals. If m and n are positive integers and the ratio m/n is expressed as a decimal, is m/n a terminating decimal?
(1) 75 < m < 90
(2) n = 8

Please help me explain the logic ?

Thnx for help
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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Feb 20, 2013 11:05 pm
rajat27 wrote:Any decimal that has only a Â…infnite number of nonzero digits is a terminating decimal. For example, 16, 0.73, and 3.178 are three terminating decimals. If m and n are positive integers and the ratio m/n is expressed as a decimal, is m/n a terminating decimal?
(1) 75 < m < 90
(2) n = 8
Always remember that any fraction whose denominator has only 2 and/or 5 as prime factors can be expressed as a terminating decimal. Otherwise, for example if the denominator has 3 or 7 or 11 etc as its prime factor, then the fraction can not be expressed as a terminating decimal.

Statement 1: We don't know anything about the denominator. --> Not sufficient

Statement 2: As the denominator is only power of 2, the fraction can be expressed as terminating decimal irrespective of the numerator. --> Sufficient

The correct answer is B.
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by ceilidh.erickson » Thu Feb 21, 2013 11:33 am
Anurag is right, but it's also helpful to think about why this is true...

Our entire numerical system is based on 10s (because we have 10 fingers, and that's what cavemen started counting on). Every time we multiply or divide by a power of 10, we change the decimal placement:
0.001
0.01
0.1
1
10
100
1,000

When we divide by things that contain the factors of 10 (2 and 5), the decimal will resolve itself, because decimals are all based on 10s. Some power of 10 (100; 10,000; 100,000,000) will be divisible by that number. If it has any prime factors that don't go into 10 (3, 7, 11, etc), then we can say the decimals don't "like" it, because no power of 10 will ever be divisible by that number.
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by GMATGuruNY » Thu Feb 21, 2013 11:54 am
Other problems that test the same concept:

https://www.beatthegmat.com/real-number- ... 61902.html
https://www.beatthegmat.com/terminating- ... 08208.html
https://www.beatthegmat.com/terminating- ... 92476.html
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