Math Problem Statement

Allison measured a line to be 18.6 inches long. If the actual length of the line is 17.9 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

Solution

To calculate the percent error of Allison's measurement, we use the formula:

Percent Error=(Measured ValueActual ValueActual Value)×100\text{Percent Error} = \left(\frac{\left|\text{Measured Value} - \text{Actual Value}\right|}{\text{Actual Value}}\right) \times 100

Given:

  • Measured Value = 18.6 inches
  • Actual Value = 17.9 inches

Now, let's calculate it:

Percent Error=(18.617.917.9)×100=(0.717.9)×1003.91%\text{Percent Error} = \left(\frac{|18.6 - 17.9|}{17.9}\right) \times 100 = \left(\frac{0.7}{17.9}\right) \times 100 \approx 3.91\%

To the nearest tenth of a percent, the percent error is 3.9%.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What would the percent error be if the measured value was 19.0 inches?
  2. How can percent error help in assessing the accuracy of a measurement?
  3. How does the size of the actual value affect the percent error?
  4. Can a percent error be negative? Why or why not?
  5. What is the percent error if the measured value and the actual value are the same?

Tip: Percent error gives you an idea of how close your measurement is to the actual value, helping to identify potential errors.

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Math Problem Analysis

Mathematical Concepts

Measurement
Percent Error

Formulas

Percent Error formula

Theorems

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Suitable Grade Level

Grades 7-9