Find the 2007th digit after the decimal point representation of 200/7.

Question

Find the 2007th digit after the decimal point representation of 200/7.

 

Answer 1

All decimal representations of integers divided by 7 have an infinitely repeating group of 6 digits.  For example, 1/7 = 0.142857... and 4/7 = 0.571428...

200 / 7 = 28 with remainder 4, so the decimal part of this answer is infinitely repeating groups of 571428.

 

2007th digit (after decimal point) can be determined by observing that 2007 / 6 = 334 with remainder 3. So there are 334 6-digit groupings (572814) followed by 571; therefore 1 must be the 2007th digit in the infinitely repeating set of digits 571428.

 

Answer: 1

Answer 2

200 / 7 is 28.571428 repeating. Just use the repeating part after the decimal to solve for the 2007th digit.