Is 0.323232 a rational number

Answer 1

A rational number is one which can be expressed by a division of a/b where both a and b are integers. In this case, we have a repeating decimal. All repeating decimals are rational numbers, and so we can say 0.323232.... is a rational number. The proof is as follows:

0.323232... x 100 = 32.323232...

0.323232... x 100 - 0.323232.... = 32

0.323232... x 99 = 32

0.323232... = 32/99

Thus 0.323232.... can be expressed as the fraction 32/99, and so is rational.