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

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

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

### 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.

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

### Step 2: Calculate the percentage error

\[
\text{Percentage Error} = \left(\frac{0.005 \text{ m}}{4.22 \text{ m}}\right) \times 100
\]

\[
\text{Percentage Error} = \left(\frac{0.005}{4.22}\right) \times 100 \approx 0.11848\% 
\]

### Step 3: Round to 2 decimal places

\[
\text{Percentage Error} \approx 0.12\%
\]

So, the percentage error is **0.12%**.

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

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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.

Learn how to calculate percentage error for a measurement of 4.22m, rounded to the nearest centimeter. Detailed steps and formula application included. Suitable for Grades 9-12.

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