A hip replacement part measures 24.75 cm and the blue-print specifies the part is 24.72 cm. What is the relative 
error and percent error?

To find the **relative error** and the **percent error**, we'll use the following formulas:

### 1. **Relative error**:
\[
\text{Relative error} = \frac{|\text{Measured value} - \text{True value}|}{\text{True value}}
\]

### 2. **Percent error**:
\[
\text{Percent error} = \text{Relative error} \times 100
\]

Where:
- Measured value = 24.75 cm
- True (blueprint) value = 24.72 cm

### Step 1: Calculate the relative error
\[
\text{Relative error} = \frac{|24.75 - 24.72|}{24.72} = \frac{0.03}{24.72} \approx 0.00121
\]

### Step 2: Calculate the percent error
\[
\text{Percent error} = 0.00121 \times 100 = 0.121\%
\]

### Final Results:
- **Relative error** = 0.00121
- **Percent error** = 0.121%

Would you like further clarification or details?

Here are five related questions for practice:
1. What would the relative error be if the measured value was 25.00 cm?
2. How does the relative error change if the true value decreases?
3. Can you calculate the percent error if the measured value is smaller than the true value?
4. What would be the relative error if the measured and true values are exactly equal?
5. How do you handle errors in cases where values are measured in millimeters?

**Tip**: When calculating percent error, always express the result as a positive value, even if the measured value is smaller than the true value.

A hip replacement part measures 24.75 cm and the blue-print specifies the part is 24.72 cm. What is the relative error and percent error?

Learn how to calculate the relative error and percent error for a hip replacement part with a measured value of 24.75 cm and a blueprint value of 24.72 cm. This detailed guide explains key error analysis concepts and provides formulas for solving similar problems. Suitable for students in Grades 8-10.

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