Math Problem Statement

Calculate the percentage error of a measurement of 4.22m, measured to the nearest cm. Round to 2 decimal places

Solution

To calculate the percentage error, we'll use the following formula:

Percentage Error=(Absolute ErrorMeasured Value)×100\text{Percentage Error} = \left(\frac{\text{Absolute Error}}{\text{Measured Value}}\right) \times 100

Step 1: Determine the absolute error

Since the measurement is given to the nearest centimeter (0.01 meters), the absolute error is half of the smallest unit of measurement.

Absolute Error=0.01 m2=0.005 m\text{Absolute Error} = \frac{0.01 \text{ m}}{2} = 0.005 \text{ m}

Step 2: Calculate the percentage error

Percentage Error=(0.005 m4.22 m)×100\text{Percentage Error} = \left(\frac{0.005 \text{ m}}{4.22 \text{ m}}\right) \times 100

Percentage Error=(0.0054.22)×1000.11848%\text{Percentage Error} = \left(\frac{0.005}{4.22}\right) \times 100 \approx 0.11848\%

Step 3: Round to 2 decimal places

Percentage Error0.12%\text{Percentage Error} \approx 0.12\%

So, the percentage error is 0.12%.

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


Here are some related questions you might find useful:

  1. What is the concept of absolute and relative error?
  2. How do you calculate percentage error for different types of measurements?
  3. What factors affect the accuracy of a measurement?
  4. How does rounding affect percentage error?
  5. What is the difference between precision and accuracy?
  6. Can you calculate the percentage error for a measurement with a different unit?
  7. What is the significance of significant figures in error calculation?
  8. How does the unit of measurement impact the percentage error?

Tip: Always consider the smallest unit of measurement when calculating percentage error, as it significantly affects the accuracy of your result.

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Math Problem Analysis

Mathematical Concepts

Measurement
Error Analysis
Percentage

Formulas

Percentage Error Formula: (Absolute Error / Measured Value) * 100

Theorems

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Suitable Grade Level

Grades 9-12