Why is 0.57575757 irrational?

Answer 1

NO!!!! It is NOT irrational. Reason, it can be converted to a Ratio(fraction).

How do I know???

1. You have not indicated that the decimals go to inifinity.

2. There is a regular order in the digits.

As given it is a terminal decimal 0.57575757

If it was an infinite decimal it should read 0.57575757... ( Note the dots that indicate it contiunes to infinity.

As a terminal decimal its fraction is 57575757/100000000 Ugh!!!!

As an infinite decimal it can be converted to a ratio(fraction)

Hence

Let P = 0.57575757...

&

100P = 57.57575757....

Subtract

99P = 57 ( Notice the repeating decimals subtract to zero.

P = 57/99

Cancel down by '3'

P = 19/33 THe answer

0.575757... = 19/33

&

0.57575757 = 57575757/100000000

Answer 2

Actually, the number is rational. So the question is nonsense.