Problem Solving

Hi there,

I've been doing some practice tests, and this question has just cropped up.


When 4/7 is expressed as a decimal, what is the 38th digit to the right of the decimal point?


8
7
5
3
1



I choose answer B - 7 as a strategic guess, fortunately it's correct! But I can't see how I could do the math to figure this out...

The answer explanation is as so:

"4/7 expressed as a decimal gives a result of 0.571428 repeating, which is a pattern that repeats every 6th term. To solve, we need to find where the 38th term would fit into this pattern. This can be done by solving for the remainder when 38 is divided by 6. If the remainder is zero, then we're looking for the sixth term in the sequence. Otherwise we're looking for the term that corresponds to the remainder. 38 divided by 6 = 6, remainder 2. The remainder of 2 means that we're looking for the second term in the pattern 0.571428. The second term is 7, so (B) is correct"

Without a calculator, I can't divide 4/7 to achieve the result of 0.571428 repeating.. How would that come to me..?! Please help!


Many thanks

Hi Gemmox

You need to use long division on your GMAT scrap paper and keep dividing until you see a pattern. In this case you have already noticed a pattern 0.571428 571428 571428 and so on. (on exam day once you see the 5 you can stop because the patter will repeat but I have written it just for demo).

Since the pattern repeats every 6th term, on 36th position will be 8 and 38th position will be 7.

Hope that helps.

Hi melguy,

Your response is most appreciated! I see the strategy behind it now, and certainly didn't think to recognise the repeating 5!

Many thanks again!

gemmox wrote:Hi there,

I've been doing some practice tests, and this question has just cropped up.


When 4/7 is expressed as a decimal, what is the 38th digit to the right of the decimal point?


8
7
5
3
1



I choose answer B - 7 as a strategic guess, fortunately it's correct! But I can't see how I could do the math to figure this out...

The answer explanation is as so:

"4/7 expressed as a decimal gives a result of 0.571428 repeating, which is a pattern that repeats every 6th term. To solve, we need to find where the 38th term would fit into this pattern. This can be done by solving for the remainder when 38 is divided by 6. If the remainder is zero, then we're looking for the sixth term in the sequence. Otherwise we're looking for the term that corresponds to the remainder. 38 divided by 6 = 6, remainder 2. The remainder of 2 means that we're looking for the second term in the pattern 0.571428. The second term is 7, so (B) is correct"

Without a calculator, I can't divide 4/7 to achieve the result of 0.571428 repeating.. How would that come to me..?! Please help!


Many thanks

The appearance of this problem means that your math skills are really good!

4/7 = 0.571428 recurring.
So 38th digit would be (38 mod 6)th digit to the right of the decimal point = 2nd digit to the right of the decimal point = 7

Now to answer your question, to calculate n/7 is fairly simple:
1/7 = 0.142857
2/7 = 0.285714
3/7 = 0.428571
4/7 = 0.571428
5/7 = 0.714285
6/7 = 0.857142
If you observe the above numbers carefully, they are all a rotated version of 142857, and the first two digits are close to the multiples of 14.
So if you are asked 4/7, calculate 14 * 4 = 56 and rotate 142857 to 571428.
This gives 4/7 = 0.571428

Cheers