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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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Math Expert
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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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Math Expert
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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
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.
Re: What is the 25th digit to the right of the decimal point in   [#permalink] 29 Apr 2015, 08:37
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