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\(\frac{2}{9} = 0.222222222...........2\)

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

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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\(\frac{2}{9}\) = 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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\(\frac{2}{9}\) + \(\frac{3}{11}\) = \(\frac{49}{99}\)

\(\frac{49}{99}\) = 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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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: https://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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Bunuel
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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

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

Answer: C.

For more on converting a recurring decimal to fraction check this: https://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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carcass
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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