Show that 30.1111 ... is a rational number.

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.