Is 0.272727 rational or irrational

RATIONAL , because you can convert it to a RATION (FRACTION).

Method

Let P = 0.272727....

Then

100P = 27.272727....

Subtract

99P = 27 (Note the decimals to infinity subtract to zero.

P = 27/99

Cancel down by '9'

P = 3/11 ( Which is a RATIO/rational).

Since both '3' & '11' are prime numbers this will not cancel down any further.

Hence 3/11 = 0.272727....