Question

What is the 2007th digit to the right of the decimal point in the decimal expansion of 1/7?

Answer 1

decimal expansion of 1/7 is 0.14285714285

Notice the 6th digit is 7, the 7th digit is 1, the 8th digit is 4, etc…

Therefore, you just divide which digit you want to know by 6, then look at the digit of the remainder. If the remainder is 0, then you are looking at the 6th digit.

For example if you want to know the 13th digit, 13/6 = 2 remainder 1. Therefore, you look at the first digit.

so for 2007 th digit we have,

Answer: 2007/6= 334 , remainder 3, so we look at third digit , which is 2