Math Problem Statement

Traedyn measured the outside temperature with his thermometer. The actual temperature outside was 68 Fahrenheit he took two measurements: measurement 1: 70.4 Fahrenheit and measurement 2: 67.3 Fahrenheit what is the percent error of measurements 1 and 2?

Solution

To calculate the percent error for each measurement, we can use the formula:

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

Given:

  • Actual Temperature = 68°F
  • Measurement 1 = 70.4°F
  • Measurement 2 = 67.3°F

Percent Error for Measurement 1:

Percent Error=(70.46868)×100=(2.468)×1003.53%\text{Percent Error} = \left( \frac{|70.4 - 68|}{68} \right) \times 100 = \left( \frac{2.4}{68} \right) \times 100 \approx 3.53\%

Percent Error for Measurement 2:

Percent Error=(67.36868)×100=(0.768)×1001.03%\text{Percent Error} = \left( \frac{|67.3 - 68|}{68} \right) \times 100 = \left( \frac{0.7}{68} \right) \times 100 \approx 1.03\%

Final Results:

  • Percent Error for Measurement 1: ≈ 3.53%
  • Percent Error for Measurement 2: ≈ 1.03%

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. How would percent error change if the measurements were in Celsius instead of Fahrenheit?
  2. What are other ways to measure the accuracy of temperature readings?
  3. How can environmental factors affect thermometer measurements?
  4. Can rounding affect the accuracy of percent error calculations?
  5. What is the difference between percent error and percent difference?

Tip: When dealing with percent error, always ensure that you use the absolute difference to avoid negative errors.

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Math Problem Analysis

Mathematical Concepts

Percent Error
Absolute Value
Accuracy in Measurements

Formulas

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

Theorems

Absolute Difference

Suitable Grade Level

Grades 6-8