What is the 21st digit in the decimal expansion of 723 What

What is the 21st digit in the decimal expansion of 7/23? What is the 5280th digit in the decimal expansion of 10/17? The 21st digit in the decimal expansion of 7/13 is The 5280th digit in the decimal expansion of 10/17 is.

Solution

a) 7/13 = 0,5384615...

the digits repeat after every 6 digits

21/6 = 3 and remainder is 3

so, 21st digit would be 8

b) 10/17 = 0.58823512941764705....

he digits repeat after every 16 digits

5280/16 = 330 and remainder is 0

so, 5280th digit would be 0