To find the percent error of Emily's estimate, we need to follow two main steps:
1. Calculate the absolute error.
2. Convert the absolute error into a percent error.
**Step 1: Calculate the Absolute Error**
The absolute error is the difference between the estimated number and the actual number without considering the direction of the error (we do not care if it was an overestimate or an underestimate).
Let `estimated_students` be the estimated number of students and `actual_students` be the actual number of students. The absolute error (`absolute_error`) is calculated as:
\[ \text{absolute_error} = |\text{actual_students} - \text{estimated_students}| \]
Substitute the given values:
\[ \text{absolute_error} = |350 - 315| \]
\[ \text{absolute_error} = |35| \]
Since the absolute value of any number is non-negative:
\[ \text{absolute_error} = 35 \]
Emily was off by 35 students.
**Step 2: Calculate the Percent Error**
The percent error compares the absolute error to the actual number, giving us a sense of how large the error is in relation to the actual value. The formula for the percent error (`percent_error`) is:
\[ \text{percent_error} = \left( \frac{\text{absolute_error}}{\text{actual_students}} \right) \times 100\% \]
Substitute the known values:
\[ \text{percent_error} = \left( \frac{35}{350} \right) \times 100\% \]
To compute this, first do the division:
\[ \text{percent_error} = 0.1 \times 100\% \]
\[ \text{percent_error} = 10\% \]
Therefore, Emily's percent error in estimating the number of students at the soccer game is 10%.