https://file.aiquickdraw.com/mathbot/file/1739027982032hj08iplo.jpg

The image shows a math problem related to absolute and relative errors. Let's break it down:

### The scenario:
- The book is believed to be worth $1,550, but the actual value is $975 (since it was a 1st edition printed in English, not the actual 1st edition).
- The task asks for:
  - The **Absolute Error**.
  - The **Relative Error** (rounded to two decimal places).

### Definitions:
- **Absolute Error**: The difference between the measured value and the actual value.
  \[
  \text{Absolute Error} = |\text{Measured Value} - \text{Actual Value}|
  \]
  
- **Relative Error**: The ratio of the absolute error to the actual value, expressed as a percentage.
  \[
  \text{Relative Error} = \frac{\text{Absolute Error}}{\text{Actual Value}} \times 100
  \]

### Now, let's calculate:

#### a. Absolute Error:
\[
\text{Absolute Error} = |1550 - 975| = 575
\]

#### b. Relative Error:
\[
\text{Relative Error} = \frac{575}{975} \times 100 \approx 58.97\%
\]

### Final answers:
a. The **Absolute Error** is $575.

b. The **Relative Error** is approximately 58.97%.

Let me know if you need further clarification or additional steps! 

### Follow-up questions:
1. How do absolute and relative errors impact the accuracy of a measurement?
2. What other examples can we use to calculate absolute and relative errors?
3. How does rounding affect the calculation of relative error?
4. In what fields are absolute and relative errors commonly used?
5. How would you calculate relative error if the measured value was higher than the actual value?

**Tip:** Always ensure your actual and measured values are clearly defined before starting error calculations!

On Pawn Stars, a man brought in a 1st edition copy of Henry David Thoreau's book Walden. He believed the book was worth around $1550. To confirm this was authentic, the guys brought in an expert. She confirmed it was a 1st edition... but unfortunately, it was only the 1st edition printed in English and not the actual 1st edition. This made the actual value closer to $975.

SHOW ALL YOUR WORK FOR BOTH PARTS ON YOUR PAPER!

a. What is the Absolute Error? State your answer as a complete sentence. (3 points)
b. What is the Relative Error? Round to 2 decimal places. (3 points)

Solve a practical math problem involving the absolute and relative error of a book's valuation. Learn step-by-step how to calculate the absolute error of $575 and the relative error of approximately 58.97%. This example is perfect for middle school students (Grades 6-8) exploring error calculations.

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