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

Organise the following values into two groups of values less than 10% and values greater than 10%:

$19\%,0.9,0.09,\frac{19}{100},\frac{1}{11}$

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:

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

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