Which of the following fractions has the greatest number of

Question

Which of the following fractions has the greatest number of repeating digits? (For example, 1/3 = 0.333... has 1 repeating digit and 1/11 = 0.090909... has 2 repeating digits.)

A. 2/3
B. 5/6
C. 6/7
D. 8/9
E. 10/11

bb · Answer

Moving this to the PS sub-forum as well

Krunaal · Answer

A. 2/3 = 0.6666... => 1 repeating digit

B. 5/6 = 0.8333... => 1 repeating digit

D. 8/9 = 0.8888... => 1 repeating digit

E. 10/11 = 0.9090... => 2 repeating digits

Now option C. is not a terminating decimal, since in its base form it has  7  in the denominator, and it  must have more than 2 repeating digits since there can only be one valid answer from available answer choices.

Answer C.

Peterparker2 · Answer

How did we arrive at that conclusion that C is not a terminating decimal without solving? Also since we'll have just two minutes to solve the problem in exam how can we solve the other fractions to decimal very quickly?

Krunaal · Answer

1. When  denominator of the reduced fraction has at least one prime factor that is neither 2 nor 5, it is a non-terminating / recurring decimal. Here's a link to  theory on terminating and repeating decimals  and  collection of questions on terminating decimals .

2. It is generally worth to memorize some fraction-decimal equivalents, it will help save time on certain quant questions. Memorize decimals of 1/11, 1/10, 1/9, 1/8,.......till 1/2. For 2/3 you just have to multiply 2 to 1/3 => 2*0.333... = 0.666... Similarly for option D. and E. For 5/6 = 1 - 1/6 = 1 - 0.1666...

Another way is to see if you can bring 9 in denominator, the number of 9s in the denominators is the number of repeating digits in a non-terminating decimal. In this particular problem: 2/3 = 6/9 =>  one 9, one repeating digit ; 5/6 = 75/90 =>  one 9, one repeating digit ; 10/11 = 90/99 =>  two 9s, two repeating digits

Hope it helps.

Peterparker2 · Answer

Hi, 
What's the significance of bringing 9 in denominator? Also won't option C have one 9 too then? 6/7=42/49?
Also after memorisation I assumed 6/7=0.857, how can I determine that these digits will be repeating? Can't they be non repeating too?

Krunaal · Answer

Check out converting recurring decimal to a fraction in Math Number Theory - we are using the same concept. The denominator is of the form 10^n - 10^m where n and m are non-negative integers and n > m . eg. 99, 90, 9900, etc. A fraction in its lowest term can be expressed as a terminating decimal if and only if the denominator has powers of only 2 and/or 5. Here's the theory on the concept: https://gmatclub.com/forum/how-to-ident ... 88087.html

bumpbot · Answer

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Which of the following fractions has the greatest number of

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Which of the following fractions has the greatest number of

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