is 0.133134135... rational or irrational? Also is it terminating or reapeating?
The number 0.133134135... is rational and repeating.
To see why it is rational, note that the repeating pattern is a block of digits 133. Therefore, if we let x = 0.133134135..., we can multiply both sides of the equation by 1000 to obtain 1000x = 133.134135..., and subtracting the equations eliminates the repeating decimal part: 1000x - x = 133 - 0.133 = 132.867. Simplifying, we have 999x = 132.867, and dividing both sides by 999 yields x = 132.867/999 = 0.133.
Since we can express 0.133134135... as the ratio of two integers (1 and 7), it is a rational number.
Furthermore, it is repeating because the sequence of digits 133 repeats indefinitely after the decimal point.