Find the absolute and relative errors in the following situation.
Your true height is 61.0 inches ​(5 ' 1 ''), but a nurse in your​ doctor's office measures your height as 61.4 inches.

To find the **absolute error** and **relative error**, we'll follow these steps:

### 1. **Absolute Error:**

The absolute error is the difference between the measured value and the true value.

\[
\text{Absolute Error} = |\text{Measured Value} - \text{True Value}|
\]

In this case:
- True height = 61.0 inches
- Measured height = 61.4 inches

\[
\text{Absolute Error} = |61.4 - 61.0| = 0.4 \text{ inches}
\]

### 2. **Relative Error:**

The relative error is the absolute error divided by the true value, often expressed as a percentage.

\[
\text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}} \times 100
\]

Substituting the known values:

\[
\text{Relative Error} = \frac{0.4}{61.0} \times 100 \approx 0.6557\%
\]

### Final Answers:
- **Absolute Error:** 0.4 inches
- **Relative Error:** approximately 0.656%

Would you like further details or clarifications?

### 5 Related Questions:
1. How does the size of the absolute error change with larger true values?
2. When would a small absolute error still result in a large relative error?
3. How would the errors change if your true height were 70 inches instead?
4. What are the typical uses of relative error in measurement applications?
5. How does rounding affect the calculation of relative error?

**Tip:** Always ensure to double-check units when calculating absolute and relative errors, especially when conversions are involved.

Find the absolute and relative errors in the following situation. Your true height is 61.0 inches (5 ' 1 ''), but a nurse in your doctor's office measures your height as 61.4 inches.

Learn how to find the absolute and relative errors in a height measurement scenario where the true height is 61.0 inches and the measured height is 61.4 inches. This problem covers key concepts such as absolute error and relative error, suitable for students in Grades 6-8.

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