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# What is the 25th digit to the right of the decimal point in

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What is the 25th digit to the right of the decimal point in [#permalink]  13 Aug 2012, 06:06
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What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Practice Questions
Question: 20
Page: 154
Difficulty: 600
[Reveal] Spoiler: OA

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Re: What is the 25th digit to the right of the decimal point in [#permalink]  13 Aug 2012, 06:06
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Expert's post
SOLUTION

What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

$$\frac{6}{11}=0.5454...$$.

Every odd-numbered digit, to the right of the decimal point, is 5, thus 25th (odd) digit will also be 5.

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Re: What is the 25th digit to the right of the decimal point in [#permalink]  13 Aug 2012, 06:52
6/11=0.54545454 repeating, with 5 occuring at 1,3,5,7 etc. So the 25th digit will be 5.
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  16 Aug 2012, 10:48
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C) 5
Same solution as above, but in case the repeating digits are more numerous then see:
1) Number of repeating digits (in this case 2 -> .5454..)
2) Divide the # of the digit you're supposed to view (25th digit) by # of repeats = (25/2)th digit
3) If no remainder, then its 4, if there's a Remainder = 1 then it has to be the next digit or 5, as in this case
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  16 Aug 2012, 11:35
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6/11 results in a Non-terminating decimal equal to .545454......54
Every even place (2nd,4th,6th,,,,,,,,,24th) digit is 4.
Every Odd place (1,3,5.....25) digit is 5.
Thus thus the odd place digit is 5
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  17 Aug 2012, 00:12
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Expert's post
SOLUTION

What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

$$\frac{6}{11}=0.5454...$$.

Every odd-numbered digit, to the right of the decimal point, is 5, thus 25th (odd) digit will also be 5.

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Re: What is the 25th digit to the right of the decimal point in [#permalink]  02 Aug 2013, 12:07
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an easy way to find 6/11 in decimal terms

expand it by 9

(6*9)/(11*9) = 54/99

note that 54/99 is the fractional representation of circulating (recurring) decimal 0,545454...

___

I dunno how anyone else would of got 0.5454 etc without using a calculator
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  03 Nov 2013, 12:13
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But is there anyway to remember how to calculate 6/11 or 7/11 for that matter?I can't possibly remember all fractions...
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  03 Nov 2013, 12:18
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Expert's post
Markster wrote:
But is there anyway to remember how to calculate 6/11 or 7/11 for that matter?I can't possibly remember all fractions...

Try to simply divide 6 by 11 to get 0.5454...

Else notice that 6/11=54/99=0.5454... Check Converting Decimals to Fractions here: math-number-theory-88376.html
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  09 Sep 2014, 22:57
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Bunuel wrote:
What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Practice Questions
Question: 20
Page: 154
Difficulty: 600

multiply 9 on both 6 & 11 then u will get 54/99...

whatever 2 digit number divided 99 will have the same digits repeat... say here 0.5454....

25th digit will be 5....
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  29 Apr 2015, 05:29
Just want to be clear here. Are we expected to know non terminating fractions or expected to do the math of 6/11? I could do, but I felt it would be math intensive and wanted to avoid that. The rule that seemed relevant from the number theory link is that terminating fractions have a denominator that fits the 2^m*5^n formula. What's the best way to approach this, and what math is unnecessary? Please advise.
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  29 Apr 2015, 08:37
I divided 6/11 and got to .545, after that I realized the pattern would repeat itself. As there's just two different digits the even decimals will be 5 and the odds will be 4. Thus 5 is the answer and C as the answer choice.
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Re: What is the 25th digit to the right of the decimal point in [#permalink]  04 May 2015, 18:39
Expert's post
Hi braveally,

The GMAT cannot realistically expect you to work through 25 digits one at a time, so this question MUST have a pattern to it.

There are certain pieces of information that you're expected to have memorized (formulas, math and grammar rules, etc.) and other types of information that would be beneficial to have memorized (fraction-to-decimal conversions, commonly tested 'patterns', etc.). It shouldn't be difficult to memorize the decimal equivalent of a set of fractions, BUT if you don't want to, then that's fine - the work will just take a little longer.

So the question in this case becomes "how quickly can you mathematically determine that 6/11 = .5454 repeating?" You were concerned that the work would be time-sensitive, so you didn't attempt it. But I'm curious about how quickly you COULD have done it. Grab a timer and find out. I bet it takes 10-15 seconds (at most) until you have the proof that you need.

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Re: What is the 25th digit to the right of the decimal point in   [#permalink] 04 May 2015, 18:39
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# What is the 25th digit to the right of the decimal point in

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