Math Problem Statement

Tommy measures a wall as 13.5 feet, when in reality it is 15 ft. What's his percent error?

Solution

The formula for percent error is:

Percent Error=(Measured ValueActual ValueActual Value)×100\text{Percent Error} = \left( \frac{|\text{Measured Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100

Plugging in the values:

Percent Error=(13.51515)×100\text{Percent Error} = \left( \frac{|13.5 - 15|}{15} \right) \times 100

=(1.515)×100= \left( \frac{1.5}{15} \right) \times 100

=(0.1)×100= (0.1) \times 100

=10%= 10\%

So, Tommy's percent error is 10%.

Would you like a deeper explanation or have any questions?

Related Questions:

  1. How do you determine if a measurement is an overestimate or underestimate?
  2. What are other common real-life scenarios where percent error is useful?
  3. How does percent error differ from percentage change?
  4. What are some ways to reduce measurement errors in practical applications?
  5. How does percent error relate to accuracy and precision in scientific experiments?

Tip:

Percent error is always taken as a positive value, as it represents the magnitude of the error regardless of whether it is an overestimate or underestimate.

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Math Problem Analysis

Mathematical Concepts

Percent Error
Measurement Accuracy
Basic Arithmetic

Formulas

Percent Error = (|Measured Value - Actual Value| / Actual Value) × 100

Theorems

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Suitable Grade Level

Grades 6-8