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So I was doing my math homework, and I had to find the 4,000th digit in the decimal form of 1/175. I found out the 4,000th digit was 7 by dividing 1 by 175, which is 0.00\overline{571428}. I did 2 + x * 6, in which I found x to be 666. Then plugging x into the equation I found that the answer was 3998. Then I found that the 4,000th digit was 7. Is there like another method to solving this problem without using a calculator? Maybe perhaps do some math magic on 1/175? Thanks for the help!

 May 3, 2020
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It looks fine to me the way you did it. If you knew a progaramming language, you could write a very simple counting routine, in which case it would do it for you in about 1 millisecond. Whether that would be acceptable to your Math Teacher or not is a different matter.

 May 3, 2020
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Oh, okay, thanks!

 May 4, 2020

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