I came across the following question on MGMAT
If the fraction d were converted into a decimal, would there be more than 3 nonzero digits to the right of the decimal point?
(1) The denominator of d is exactly 8 times the numerator of d.
(2) If d were converted into a decimal, d would be a non-repeating decimal.
OA is A
It was easy for me to spot the answer but got confused after reading about non-repeating decimal. https://www.mathwithlarry.com/lessons/lesson091.htm
non-repeating decimals:- These are decimal numbers that go on forever, but do not follow a pattern at all. An example might be 0.48376922026985321.... If there is no pattern, and no end in sight, it means that the number is a non-repeating decimal.
If I keep this in my mind, then statement 2 can be considered as the correct answer i.e d would be a non-repeating decimal (decimal numbers that go on forever, but do not follow a pattern at all).
So, there would there be more than 3 nonzero digits to the right of the decimal point.
Please help me in understanding this theory. I am a bit confused now.
Thanks & Regards
Sachin
non-repeating decimal
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- sachin_yadav
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A) alone is sufficient.
As let Numerator = x then denominator = 8x.
Hence,D=x/8x or 0.125.
B) As per B,decimals are non-repeating,which means the digits after decimal are unique and do not repeat in a pattern.But fails to comment on the number of digits.
Additionally,Repeating decimals are obtained when a number is divided by 9 or any multiple of 9 (9,99,999...)
for ex 2/9 = .2222..
Also known as non-terminating decimals.
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As let Numerator = x then denominator = 8x.
Hence,D=x/8x or 0.125.
B) As per B,decimals are non-repeating,which means the digits after decimal are unique and do not repeat in a pattern.But fails to comment on the number of digits.
Additionally,Repeating decimals are obtained when a number is divided by 9 or any multiple of 9 (9,99,999...)
for ex 2/9 = .2222..
Also known as non-terminating decimals.
Click on Thanks button if you find my response useful.
- Atekihcan
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That's a true statement but not an exhaustive one.aaggar7 wrote:Additionally,Repeating decimals are obtained when a number is divided by 9 or any multiple of 9 (9,99,999...)
Repeating decimals are obtained when the denominator of a rational number is not entirely made up of 2 and/or 5.
So, any number when divided by 3, 7, 11, 13, ... etc or their multiples will always result in a repeating decimal.
For example,
- 1/3 = 0.333333333....
1/7 = 0.142857142857...
1/11 = 0.09090909...
To clarify things three type of decimals are
- Terminating Decimal : Which do not go on forever. For example, 0.1 or 0.345 or 0.002005 etc. The denominator of the fractional form of these decimals will have only 2 and 5 as the prime factors.
Repeating Decimals : Which goes on forever but there is a pattern. Already discussed the examples and how to identify them.
Non-repeating Decimals : Which goes on forever but there is no pattern. These are basically the decimal representation of irrational numbers (whereas the previous two types are of rational numbers) like √2, √3, etc and π. For example, √2 = 1.4142135623... or π = 3.1415926535... goes on forever without any pattern.
Now, to answer your query regarding statement 2, I think statement 2 is indeed sufficient because by definition a non-repeating decimal will have infinite number of non-zero digits to the right of the decimal point. If it has a finite number of non-zero digits to the right of the decimal point, it will become a terminating decimal.
I feel the problem means to say "If d were converted into a decimal, d would be a terminating decimal." as statement 2.
Hope that helps.
- sachin_yadav
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Thanks Atekihcan.Atekihcan wrote: Now, to answer your query regarding statement 2, I think statement 2 is indeed sufficient because by definition a non-repeating decimal will have infinite number of non-zero digits to the right of the decimal point. If it has a finite number of non-zero digits to the right of the decimal point, it will become a terminating decimal.
I feel the problem means to say "If d were converted into a decimal, d would be a terminating decimal." as statement 2.
Hope that helps.
I got your explanation. At first, i didn't read the language of the statement (2) attentively, but now it's clear. Thanks
Regards
Sachin
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Try to understand the following or plug the values in the numerator and denominator you will come to know why OA is A:-ravi_uppal2004 wrote:why is OA " A " then can someone explain ?
A) alone is sufficient.
As let Numerator = x then denominator = 8x.
Hence,D=x/8x or 0.125.
Sachin
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- kul512
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Ravi_uppal...
I think Aaggar7's statement Now, to answer your query regarding statement 2, I think statement 2 is indeed sufficient has confused you. I think there is some error in this sentence. Sentence 2 is not sufficient because number can be 2.235 also, which is a non-repeating decimal but terminates at 3 decimal digits.[/quote]
I think Aaggar7's statement Now, to answer your query regarding statement 2, I think statement 2 is indeed sufficient has confused you. I think there is some error in this sentence. Sentence 2 is not sufficient because number can be 2.235 also, which is a non-repeating decimal but terminates at 3 decimal digits.[/quote]
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