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# Which of the following is the 21st digit to the right of the decimal

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Math Expert
Joined: 02 Sep 2009
Posts: 64249
Which of the following is the 21st digit to the right of the decimal  [#permalink]

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11 Jan 2018, 20:27
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Difficulty:

55% (hard)

Question Stats:

60% (01:40) correct 40% (01:48) wrong based on 91 sessions

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Which of the following is the 21st digit to the right of the decimal place in the decimal expression of 5/22?

A. 1
B. 2
C. 5
D. 7
E. 11

_________________
Intern
Joined: 14 Mar 2017
Posts: 5
GMAT 1: 650 Q47 V33
Re: Which of the following is the 21st digit to the right of the decimal  [#permalink]

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12 Jan 2018, 17:57
For such type of question we should start dividing and try to see if a pattern emerges (which usually does).

Now, when we reach the third decimal place we notice that after that it starts repeating.

That is 5/22 = 0.2272727... So except the first decimal place there is repeating pattern. Hence, the 21st digit to the right will be 7.

Thus, the correct option is D.

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Joined: 06 Sep 2016
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Re: Which of the following is the 21st digit to the right of the decimal  [#permalink]

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16 Feb 2018, 07:22
How I am supposed to convert 5/22 into a decimal form without a calculator?
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Joined: 25 Feb 2013
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Re: Which of the following is the 21st digit to the right of the decimal  [#permalink]

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17 Feb 2018, 08:19
MvArrow wrote:
How I am supposed to convert 5/22 into a decimal form without a calculator?

HI MvArrow,

$$\frac{5}{22} = \frac{5}{2*11}=\frac{2.5}{11}$$, division by 11 should not be a challenge even without calculator.
Re: Which of the following is the 21st digit to the right of the decimal   [#permalink] 17 Feb 2018, 08:19