Digit question

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Lookingfor700GMAT: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Mon Feb 08, 2010 12:41 pm

by Lookingfor700GMAT » Sun Mar 07, 2010 9:41 am

I just went through the following question in the OG (12th ed). Please let me know how I would know that 6/11 is 0.54545454 in decimal form without a calculator. Is there a trick to know this? I know that is is roughly 54% but I wouldn't have known that the two digits of 5 and 4 are reoccuring.

What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

3
4
5
6
7

The answer is 5.

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Source: Beat The GMAT — Problem Solving | Sun Mar 07, 2010 9:41 am

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Sun Mar 07, 2010 5:43 pm

You need to perform long division to determine the recurring digits while dividing. Long division is a basic traditional method of dividing.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8188; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Mar 27, 2018 10:39 am

Lookingfor700GMAT wrote:I just went through the following question in the OG (12th ed). Please let me know how I would know that 6/11 is 0.54545454 in decimal form without a calculator. Is there a trick to know this? I know that is is roughly 54% but I wouldn't have known that the two digits of 5 and 4 are reoccuring.

What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

3
4
5
6
7

6/11 = 0.545454...

We see that all the odd-numbered digits (1st, 3rd, etc.) to the right of the decimal point are 5 and all the even-numbered digits (2nd, 4th, etc.) to the right of the decimal point are 4. Since 25 is odd, the 25th digit to the right of the decimal point is 5.

Answer: C

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