The average of $30$ numbers is $1.2$. The average of the first $20$ of them is $1.1$ and that of the next $9$ is $1$. Then the last number is:

First, find the total sum of all $30$ numbers:
$$\text{Sum of 30 numbers}=30\times 1.2=36$$

Next, find the sum of the first $20$ numbers:

$$\text{Sum of first 20 numbers}=20\times 1.1=22$$

Find the sum of the next $9$ numbers:

$$\text{Sum of next 9 numbers}=9\times 1=9$$

Sum of these $29$ numbers $(20+9)=22+9=31$.

The last ($30^{\text{th}}$) number is obtained by subtracting the sum of the $29$ numbers from the total sum of the $30$ numbers:

$$\text{Last number}=36-31=5$$