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# What is the 25th digit to the right of the decimal point in

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Manager
Joined: 10 Apr 2018
Posts: 130
GMAT 1: 600 Q44 V28
GPA: 3.56
WE: Engineering (Computer Software)
Re: What is the 25th digit to the right of the decimal point in  [#permalink]

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31 Aug 2018, 07:06
T1101 wrote:
Easy way to remember 1/11 till 10/11 is:

1/11 --> The repeating pattern is 10-1=09 so 0.09090909
2/11 --> The repeating pattern is 20-2=18 so 0.18181818
3/11 --> The repeating pattern is 30-3=27 so 0.27272727
...
10/11 --> The repeating pattern is 100-10=90 so 0.90909090

Wow, this is amazing.
Although, I did it in the same way, Bunuel did or TTP does, this approach is interesting.
Thanks for sharing this different approach.
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Manager
Joined: 10 Apr 2018
Posts: 130
GMAT 1: 600 Q44 V28
GPA: 3.56
WE: Engineering (Computer Software)
Re: What is the 25th digit to the right of the decimal point in  [#permalink]

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31 Aug 2018, 07:11
stonecold wrote:
Another way of solving this one=>
6/11=> multiply 9 to both he numerator and denominator => 54/99
hence the decimal expansion would be 0.54545454545454
Clearly the 57th digit is 5=> Smash that C

Why did we write 6/11 as 54/99 => if denominator and numerator have same number of digits and if the denominator can be written as 10^n-1 ie 9,99,999,9999 etc then we need not carry any division process . The result would be given by the numerator

E.g => 69/99 = 0.69696969...
3/9=0.33333...
158/999=0.158158158...

Thanks for sharing this. It's interesting and have never seen this approach before.
There was another post that said, multiply numerator and denominator by 9 and you will get the answer - but I could NOT grasp, exactly "how"?
Giving 3 examples besides the one we are trying to solve was really helpful and enabled me to grasp, what an earlier post was saying.
Although, I did it using the Bunuel has done, In future I would prefer this.

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The Graceful
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Every EXPERT was a beginner once...
Don't look at the clock. Do what it does, keep going
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To achieve great things, two things are needed:a plan and not quite enough time - Leonard Bernstein.
Manager
Joined: 30 May 2018
Posts: 70
Concentration: General Management, Marketing
GMAT 1: 750 Q49 V45
GPA: 3.45
WE: Other (Retail)
Re: What is the 25th digit to the right of the decimal point in  [#permalink]

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29 Sep 2018, 22:57
So , 6/11 = .54545454.........
Every Odd digit is 5 ( 1st , 3rd , 5th and so on.... ) , hence even 25th digit would be 5.
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Director
Joined: 19 Oct 2013
Posts: 513
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: What is the 25th digit to the right of the decimal point in  [#permalink]

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30 Sep 2018, 12:54
Bunuel wrote:
What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Practice Questions
Question: 20
Page: 154
Difficulty: 600

1/11 = 0.0909.....

Times 6 = 0.5454... it repeats.

Since we want to know the 25th digit then

We have 2 numbers that repeat. 24/2 means the 24th digit would be 4, hence, we know that the 25th will be 5.

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Re: What is the 25th digit to the right of the decimal point in   [#permalink] 30 Sep 2018, 12:54

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