Question

a space shuttle was launched from the earth to the moon. the average, or accepted, value of the distance of the earth to the moon is 238,857 miles, but the shuttle crew recorded that their trip took 226,316 miles. calculate the percent error of the distance to the moon. 5.25% 7.15% 3.75% 4.45%

Explanation:

Step1: Calculate the absolute error

The formula for absolute error is \(| \text{accepted value}-\text{measured value}|\).
Here, the accepted value \(a = 238857\) miles and the measured value \(m=226316\) miles.
\(\text{Absolute error}=|238857 - 226316|= 12541\) miles.

Step2: Calculate the percent error

The formula for percent error is \(\text{Percent error}=\frac{\text{Absolute error}}{\text{Accepted value}}\times100\%\).
Substitute the values: \(\text{Percent error}=\frac{12541}{238857}\times 100\%\)
\(\text{Percent error}\approx\frac{12541}{238857}\times100\%\approx 5.25\%\)

Answer:

5.25%