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# What is the 30th digit to the right of the decimal point in the decima

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Math Expert
Joined: 02 Sep 2009
Posts: 59039
What is the 30th digit to the right of the decimal point in the decima  [#permalink]

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13 Aug 2019, 02:12
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Difficulty:

15% (low)

Question Stats:

79% (00:53) correct 21% (00:52) wrong based on 62 sessions

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What is the 30th digit to the right of the decimal point in the decimal form of 3/11 ?

A. 2
B. 3
C. 5
D. 6
E. 7

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Joined: 12 Apr 2019
Posts: 274
Re: What is the 30th digit to the right of the decimal point in the decima  [#permalink]

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13 Aug 2019, 04:15
2
1
This is a question where you need to convert a rational number to a recurring decimal.

Any rational number where the denominator consists of a power of 2 or a power of 5 or a combination of these two powers, will always give a terminating decimal. Otherwise, a rational number will give a recurring decimal.

Based on this, we can say that $$\frac{3}{11}$$ will definitely give a recurring decimal.

$$\frac{3}{11}$$ = 0.272727……

The period of this recurring decimal is 2 i.e. there are 2 distinct digits which keep recurring. The first digit to the right of the decimal point is 2, the second is 7, the third is 2, the fourth is 7 and so on.
Following this pattern, we can say that the 30th digit will be 7. The correct answer option is E.

Hope this helps!
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Re: What is the 30th digit to the right of the decimal point in the decima  [#permalink]

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13 Aug 2019, 22:07
1
It is easy to solve this question if we know the value of $$\frac{1}{11}$$.
$$\frac{1}{11} = 0.0909090909...$$ i.e. a recurring decimal.

So, $$\frac{3}{11} = 0.272727272727...$$

Every second digit right of the decimal point is "7".
30th is an even spot. So, it will also be "7".

Math Expert
Joined: 02 Sep 2009
Posts: 59039
Re: What is the 30th digit to the right of the decimal point in the decima  [#permalink]

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20 Sep 2019, 01:58
Bunuel wrote:
What is the 30th digit to the right of the decimal point in the decimal form of 3/11 ?

A. 2
B. 3
C. 5
D. 6
E. 7

Video Explanation

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Joined: 18 Dec 2017
Posts: 676
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Re: What is the 30th digit to the right of the decimal point in the decima  [#permalink]

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14 Oct 2019, 21:27
Bunuel wrote:
What is the 30th digit to the right of the decimal point in the decimal form of 3/11 ?

A. 2
B. 3
C. 5
D. 6
E. 7

1/11 is 0.0909
.09*3 is .27
So what we are saying is .272727272727.....
30th digit will be 7.
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Re: What is the 30th digit to the right of the decimal point in the decima   [#permalink] 14 Oct 2019, 21:27
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