Classify Mixed Numbers: Sorting 19%, 0.9, and Fractions Above and Below 10%

To solve this problem, we'll convert each value to a decimal and compare it with $0.10$ (which represents $10\%$):

• Convert $19\%$ to a decimal: $19\% = 0.19$. Compare with $0.10$; 0.19 > 0.10.

• $0.9$ is already a decimal. Compare directly: 0.9 > 0.10.

• $0.09$ is already a decimal. Compare directly: 0.09 < 0.10.

• Convert $\frac{19}{100}$ to a decimal: $\frac{19}{100} = 0.19$. Compare with $0.10$; 0.19 > 0.10.

• Convert $\frac{1}{11}$ to a decimal: $\frac{1}{11} \approx 0.0909$. Compare with $0.10$; 0.0909 < 0.10.

Thus, the values can be grouped as follows:

Values less than $10\%$: $0.09, \frac{1}{11}$.

Values greater than $10\%$: $0.9, \frac{19}{100}, 19\%$.

The solution involves accurate conversion and comparison:

Therefore, the correct grouping is:

0.09, \frac{1}{11}<10\%

0.9, \frac{19}{100}, 19\% > 10\%