The definition of a rational number is any number that can be written as a quotient of 2 integers... in other words, a fraction. So, number 1 would be "rational because it's a fraction".
For #2
x = 8.132132132...
1000x = 8132.132132 Multiply by 100 to move decimal to end of repeating decimal
999x = 8132.132132 - 8.132132 (subtract to get rid of repeating decimal)
999x = 8124 (solve for x)
x = 8124/999 (reduce)
x = 8 132/999