Math Problem Statement

The standard definition of a quart is equal to 947 mL. Calculate the percent error of a student's measurement if she found the experimental value of the volume of one quart of water to be equal to 934 mL.

Solution

The formula to calculate percent error is:

Percent Error=(Experimental ValueAccepted ValueAccepted Value)×100\text{Percent Error} = \left( \frac{|\text{Experimental Value} - \text{Accepted Value}|}{\text{Accepted Value}} \right) \times 100

Here, the accepted value is 947 mL, and the experimental value is 934 mL.

Now, plug in the values:

Percent Error=(934947947)×100\text{Percent Error} = \left( \frac{|934 - 947|}{947} \right) \times 100 Percent Error=(13947)×100\text{Percent Error} = \left( \frac{13}{947} \right) \times 100 Percent Error1.37%\text{Percent Error} \approx 1.37\%

So, the student's percent error is approximately 1.37%.

Would you like more details on this, or do you have any questions?

Here are 5 related questions for further exploration:

  1. How would the percent error change if the experimental value were 950 mL?
  2. What is the formula for calculating absolute error?
  3. Why is percent error used in scientific measurements?
  4. How can you minimize percent error in measurements?
  5. What is the difference between percent error and percent difference?

Tip: Always double-check units when comparing values to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Percent Error
Measurement Error
Scientific Measurement

Formulas

Percent Error = (|Experimental Value - Accepted Value| / Accepted Value) × 100

Theorems

Error Analysis

Suitable Grade Level

Grades 8-10