To find the percentage of middle school students who spend more than 10 hours per week online, we can use the following formula:
\[ \text{Percentage} = \left( \frac{\text{Number of students spending more than 10 hours online}}{\text{Total number of students}} \right) \times 100 \]
In this case:
- Number of students spending more than 10 hours online = 420
- Total number of students = 500
Now, we can substitute these values into the formula:
\[ \text{Percentage} = \left( \frac{420}{500} \right) \times 100 \]
Calculating \( \frac{420}{500} \):
\[ \frac{420}{500} = 0.84 \]
Now, we multiply by 100 to convert it into a percentage:
\[ 0.84 \times 100 = 84 \]
Thus, the percentage of middle schoolers who spend more than 10 hours per week online is \( \boxed{84%} \).