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# What is the 57th digit to the right of the decimal point in the decima

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Math Expert
Joined: 02 Sep 2009
Posts: 50624
What is the 57th digit to the right of the decimal point in the decima  [#permalink]

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19 Apr 2016, 02:01
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:42) correct 22% (01:53) wrong based on 108 sessions

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What is the 57th digit to the right of the decimal point in the decimal equivalent of 13/55?

A. 2
B. 3
C. 4
D. 5
E. 6

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Re: What is the 57th digit to the right of the decimal point in the decima  [#permalink]

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19 Apr 2016, 05:56
13/55 = 0 .2363636...
36 is non-terminating repeating decimal .
The 57th digit to the right of decimal point will be 6
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Re: What is the 57th digit to the right of the decimal point in the decima  [#permalink]

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19 Apr 2016, 06:45
1
Bunuel wrote:
What is the 57th digit to the right of the decimal point in the decimal equivalent of 13/55?

A. 2
B. 3
C. 4
D. 5
E. 6

Hi,
the most important point is to get 13/55 in decimal...
Calculators are not allowed and the fraction looks very cumbersome...

convert the fraction into a slightly friendly term..
since there is a 5 in denominator, multiply both Numerator and denomintor by 2..
so $$\frac{13}{55}= \frac{13*2}{55*2}=\frac{26}{110}=(\frac{22+4}{11})*\frac{1}{10}$$
=>$$(2+\frac{4}{11})*\frac{1}{10}$$... 11 always leaves a denominator in recurring two digits with SUM as 9..
=>$$(2+.363636..)\frac{1}{10}$$ = .2363636...
ODD digits 6 and EVEN digits 3..
57th digit is ODD so ans is 6
E
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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What is the 57th digit to the right of the decimal point in the decima  [#permalink]

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19 Apr 2016, 07:39
1
Bunuel wrote:
What is the 57th digit to the right of the decimal point in the decimal equivalent of 13/55?

A. 2
B. 3
C. 4
D. 5
E. 6

13/55 => 13/(5*11)

1/5 = 0.2

1/11 = 0.09090909......

13/5 = 2.6

2.6/11 = 0.236363636...........

Now u see we are asked to find the 57th digit to the right of decimal point,

When the places are odd the digit is 6 and when the places are even the digit is 3 {Except the first digit }

57th digit will be even , so we will have the 57th digit as 6
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Re: What is the 57th digit to the right of the decimal point in the decima  [#permalink]

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19 Apr 2016, 09:23
0,2363636...

Every odd number after the zero is a 6, ans is e
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Re: What is the 57th digit to the right of the decimal point in the decima  [#permalink]

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26 Aug 2018, 08:38
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Re: What is the 57th digit to the right of the decimal point in the decima &nbs [#permalink] 26 Aug 2018, 08:38
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