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What is the 99th digit after the decimal point in the

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What is the 99th digit after the decimal point in the  [#permalink]

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New post Updated on: 10 Mar 2012, 08:41
1
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A
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C
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E

Difficulty:

  25% (medium)

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What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9
Spoiler: OA

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Originally posted by carcass on 10 Mar 2012, 08:23.
Last edited by Bunuel on 10 Mar 2012, 08:41, edited 1 time in total.
Added the OA
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Re: What is the 99th digit after the decimal point in the decim  [#permalink]

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New post 10 Mar 2012, 08:37
3
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9


\(\frac{2}{9} + \frac{3}{11}=\frac{22}{99} + \frac{27}{99}=\frac{49}{99}=0.494949...\). So, 99th (odd placed after the decimal) digit will be 4.

Answer: C.

For more on converting a recurring decimal to fraction check this: math-number-theory-88376.html

Hope it helps.
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Re: What is the 99th digit after the decimal point in the  [#permalink]

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New post 10 Mar 2012, 09:54
I have not added OA because I hoped in a more long discussion. :)

Thanks
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Re: What is the 99th digit after the decimal point in the  [#permalink]

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New post 02 Sep 2014, 23:02
2
\(\frac{2}{9} = 0.222222222...........2\)

\(\frac{3}{11}= 0.272727.............. 27\)

Addition (Does not have carries)

\(\frac{2}{9} + \frac{3}{11} = 0.4949494949....... 49\)

Odd's have 4

99th would have 4

Answer = C
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Re: What is the 99th digit after the decimal point in the  [#permalink]

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New post 18 Sep 2016, 02:04
\(\frac{2}{9}\) = 0.22222.... ==> 99th digit is 2

\(\frac{3}{11}\) = 0.27272727.... ==> Every odd digit is 2. So, 99th digit will be 2.

2 +2 = 4 ( Ans C)
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What is the 99th digit after the decimal point in the  [#permalink]

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New post 18 Sep 2016, 05:23
\(\frac{2}{9}\) + \(\frac{3}{11}\) = \(\frac{49}{99}\)

\(\frac{49}{99}\) = 0.49494949..............

so the digits are getting repeated in order of two digits 49

so the 99 th digit is 4

correct answer - C
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Re: What is the 99th digit after the decimal point in the  [#permalink]

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New post 25 Jan 2018, 22:55
Bunuel wrote:
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9


\(\frac{2}{9} + \frac{3}{11}=\frac{22}{99} + \frac{27}{99}=\frac{49}{99}=0.494949...\). So, 99th (odd placed after the decimal) digit will be 4.

Answer: C.

For more on converting a recurring decimal to fraction check this: http://gmatclub.com/forum/math-number-theory-88376.html

Hope it helps.



HI what do you mean by 99th digit could you explain, I understand the theory of repeating no.'s but what do you mean by 99th Digit ?
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Re: What is the 99th digit after the decimal point in the  [#permalink]

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New post 25 Jan 2018, 23:00
hero_with_1000_faces wrote:
Bunuel wrote:
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9


\(\frac{2}{9} + \frac{3}{11}=\frac{22}{99} + \frac{27}{99}=\frac{49}{99}=0.494949...\). So, 99th (odd placed after the decimal) digit will be 4.

Answer: C.

For more on converting a recurring decimal to fraction check this: http://gmatclub.com/forum/math-number-theory-88376.html

Hope it helps.



HI what do you mean by 99th digit could you explain, I understand the theory of repeating no.'s but what do you mean by 99th Digit ?


We need 99th digit after the decimal point of 0.494949...

The first digit is 4, the second digit is 9, the third digit is 4 again, the fourth digit is 9 again, ... 99th (odd placed after the decimal) digit will be 4.
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Re: What is the 99th digit after the decimal point in the  [#permalink]

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New post 29 Jan 2018, 11:05
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9



2/9 + 3/11 = 22/99 + 27/99 = 49/99 = 0.494949….

SInce each odd-positioned digit to the right of the decimal point has a value of 4, the 99th digit is 4.

Alternate Solution:

We see that 2/9 = 0.222… and 3/11 = 0.272727…

If we add the two decimal expressions, we see that we obtain 0.494949… Since all the odd-positioned digit to the right of the decimal point has a value of of 4, the 99th digit is 4.

Answer: C
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