Question

Damian measured a line to be 9.4 inches long. If the actual length of the line is 7.8 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

Answer 1

The percent error of Damian's measurement is found using the formula: Percent Error = (|Measured Value - Actual Value| / Actual Value) x 100%. The result, rounded to the nearest tenth, is 20.5%.

Step-by-step explanation:

The question asks for the calculation of the percent error for a measurement of a line. Percent error is a way to express how accurate a measurement is compared to the actual or known value. To calculate the percent error, you use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) × 100%

For Damian's measurement:

• Measured Value = 9.4 inches
• Actual Value = 7.8 inches

First, we find the absolute difference between the measured value and the actual value:

|9.4 inches - 7.8 inches| = 1.6 inches

Then, we divide this by the actual value:

1.6 inches / 7.8 inches = 0.2051282...

Finally, we multiply by 100% to get the percent error:

0.2051282 × 100% = 20.51282%

Rounding to the nearest tenth of a percent, we have 20.5% percent error.