fundamentals of math

Question

What is the 21st digit in the decimal expansion of 5/7?

What is the 5280th digit in the decimal expansion of 7/17?

Answer 1

21st digit of 5/7 is 4

5/7 =0.714285... those 6 digits repeat endlessly, 6x3 = 18th digit is 5, 19th is 7 20th is 1, 21st is 4

7/17 =0.4117647058823529...those 16 digits repeat endlessly. 5280/16 = 330 with no remainder. the 5280th digit is 9. any nth digit that's a multiple of 16 would be 9

find how many digits repeat, divide that into the number you want, if it divides evenly, it's the same end digit. if there's a remainder, count off that many digits of the repeating sequence.