We know that 30.1111... is a rational number because it ends in repeating decimals. We can show this by writing the number as a fraction using algebra.
x = 30.1111....
10x = 301.1111....
Subtract both sides by x
10x - x = 301.1111.... - 30.1111...
9x = 271
x = 271/9
The number can be rewritten as 271/9, which you can verify is the same number by checking on a calculator.
