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What is the 2007th digit to the right of the decimal point in the decimal expansion of 4/23?

 Oct 18, 2022
 #1
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4/23 = 0.1739130434782609

 

Mmm there is a lot of digits repeating here.  You may need first of all to work out how many repeat 

I'd probably try a calculator that shows more  places or do it by hand.

 Oct 18, 2022
 #2
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+1

4/23 = 0.1739130434782608695652   1739130434782608695652    1739130434782608695652....has a "period" of 22 digits.

 

Therefore: 2007 mod 22 = 5. This means that 2007th digit is the 5th digit to the right of the decimal point, which is a "1", 0.1 7 3 9 1

 Oct 18, 2022

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