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Peterparker2
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Which of the following fractions has the greatest number of 02 Mar 2025, 12:01
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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
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Which of the following fractions has the greatest number of 02 Mar 2025, 12:05
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Moving this to the PS sub-forum as well
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Which of the following fractions has the greatest number of 02 Mar 2025, 14:13
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Peterparker2
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
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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.
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Which of the following fractions has the greatest number of 02 Mar 2025, 14:37
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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
Peterparker2
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


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.
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Which of the following fractions has the greatest number of 03 Mar 2025, 03:57
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Peterparker2
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
Peterparker2
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


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.
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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.
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Which of the following fractions has the greatest number of 03 Mar 2025, 11:42
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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

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.
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Which of the following fractions has the greatest number of 03 Mar 2025, 14:13
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Peterparker2
Hi,
What's the significance of bringing 9 in denominator? Also won't option C have one 9 too then? 6/7=42/49?
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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.


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Peterparker2

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?
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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
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