mvz2102 wrote:A question came up in the OG last night that required you to get the nth decimal of some arbitrary fraction, I believe it was 6/11.
I got the correct answer, but my method was long and difficult and involved some sketchy guesswork. Is there any way to do this for any general fraction of two integers a/b?
If that type of question appears on the GMAT, it will always involve an infinitely repeating decimal; you need to find the pattern (usually through long division), then apply the pattern to the question asked.
Let's say the question is: "What's the 113th digit to the right of the decimal point in the decimal representation of 6/11?
We think of 6/11 as "6 divided by 11" and use long division to get:
6/11 = 0.545454...
Here we see that it's a 2 digit repeating pattern - odd numbered digits are "5" and even numbered digits are "4". Since we want the 113th digit, an odd numbered digit, so it will be "5".
Here's a trickier one:
"What's the 23rd digit to the right of the decimal point in the decimal representation of 1/7?"
We think of 1/7 as "1 divided by 7" and use long division to get:
1/7 = .142857142....
Here we see that it's a 6 digit repeating pattern. We want the 23rd digit. "23/6" is "3 and 5/6"; the 5/6 tells us that we want the 5th digit in the pattern, which is "5".
edited to change "left" to "right"!
