Math Problem Statement

A student takesd the measurment 2.75 meters. Calculate the % error if the handbook states the value 3.11 meters

Solution

To calculate the percentage error, we use the following formula:

Percentage Error=(Measured ValueTrue ValueTrue Value)×100\text{Percentage Error} = \left( \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \right) \times 100

Here, the measured value is 2.752.75 meters, and the true (handbook) value is 3.113.11 meters.

Now, let's compute it:

Percentage Error=(2.753.113.11)×100\text{Percentage Error} = \left( \frac{|2.75 - 3.11|}{3.11} \right) \times 100

Percentage Error=(0.363.11)×100=11.58%\text{Percentage Error} = \left( \frac{0.36}{3.11} \right) \times 100 = 11.58\%

So, the percentage error is approximately 11.58%.

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:

  1. How is percentage error different from percentage difference?
  2. What would the percentage error be if the measured value was exactly the same as the true value?
  3. Why is it important to consider percentage error in experimental measurements?
  4. How does percentage error change if the measured value is significantly greater than the true value?
  5. Can you explain a situation where a small percentage error might still indicate a significant problem?

Tip: Always use absolute values when calculating percentage error to avoid negative results, as it’s meant to represent the magnitude of error, not the direction.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Percentage Error
Absolute Value
Error Calculation

Formulas

Percentage Error = (|Measured Value - True Value| / True Value) × 100

Theorems

-

Suitable Grade Level

Grades 8-10