Math Problem Statement

Assume that you found that the average volume of water required to fill the graduated cylinder to the 8.00 mL mark was 7.95 mL. What is the percent error?

Solution

To calculate the percent error, we use the formula:

Percent Error=(Experimental ValueTheoretical ValueTheoretical Value)×100\text{Percent Error} = \left( \frac{\text{Experimental Value} - \text{Theoretical Value}}{\text{Theoretical Value}} \right) \times 100

In this case:

  • The experimental value is the volume of water actually measured, which is 7.957.95 mL.
  • The theoretical value is the intended or accepted volume, which is 8.008.00 mL.

Now, plug in these values to find the percent error:

Percent Error=(7.958.008.00)×100\text{Percent Error} = \left( \frac{7.95 - 8.00}{8.00} \right) \times 100

Let's calculate this:

Percent Error=(0.058.00)×100=(0.00625)×100=0.625%\text{Percent Error} = \left( \frac{-0.05}{8.00} \right) \times 100 = \left( -0.00625 \right) \times 100 = -0.625\%

Since percent error is usually expressed as a positive value, we take the absolute value:

Percent Error=0.625%\text{Percent Error} = 0.625\%

Conclusion:

The percent error in measuring the volume is 0.625%.

Would you like further details or have any questions? Here are some related questions you might consider:

  1. What are some factors that could cause percent error in a volume measurement?
  2. How does the precision of the measuring instrument affect the percent error?
  3. Can percent error be greater than 100%? Under what circumstances?
  4. How would you minimize errors in a laboratory setting?
  5. What is the difference between percent error and absolute error?

Tip: Percent error helps to understand how accurate a measurement is compared to the accepted value.

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Math Problem Analysis

Mathematical Concepts

Percent Error
Experimental vs Theoretical Value

Formulas

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

Theorems

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Suitable Grade Level

Grades 9-12