Question

On average the acceleration due to gravity is 9.807m/s2 A science student measured it at 9.760m/s2. To the nearest hundeth of a percent what was the students percent error

Answer 1

To find the percent error, you can use the following formula:

\[
\text{Percent Error} = \left( \frac{\text{Experimental Value} - \text{Accepted Value}}{\text{Accepted Value}} \right) \times 100
\]

In this case:

- **Accepted Value** (average acceleration due to gravity) = \(9.807 \, \text{m/s}^2\)
- **Experimental Value** (the student's measurement) = \(9.760 \, \text{m/s}^2\)

Now, plug the values into the formula:

\[
\text{Percent Error} = \left( \frac{9.760 - 9.807}{9.807} \right) \times 100
\]

Calculating the numerator:

\[
9.760 - 9.807 = -0.047
\]

Now plug that back into the equation:

\[
\text{Percent Error} = \left( \frac{-0.047}{9.807} \right) \times 100
\]

Calculating the fraction:

\[
\frac{-0.047}{9.807} \approx -0.004785
\]

Now multiply by 100 to convert it to a percentage:

\[
\text{Percent Error} \approx -0.4785 \, \%
\]

To the nearest hundredth of a percent, the student's percent error is:

\[
\boxed{-0.48 \, \%}
\]