BMI=W/(H^2) if the errors in weight W and height H are both 1% what is percentage error of BMI

The formula for Body Mass Index (BMI) is:

\[
BMI = \frac{W}{H^2}
\]

Where:
- \(W\) is the weight,
- \(H\) is the height.

Given that the percentage errors in weight (\(W\)) and height (\(H\)) are both 1%, we need to calculate the percentage error in BMI.

### Step-by-Step Calculation:
1. **Error in Weight (\(W\)):**  
   The error in weight is directly proportional to the error in BMI. Therefore, if the error in \(W\) is 1%, it contributes 1% to the BMI error.

2. **Error in Height (\(H\)):**  
   The height \(H\) is squared in the formula, so the percentage error in height is multiplied by 2 when calculating its effect on BMI. Since the error in \(H\) is 1%, its contribution to the BMI error is \(2 \times 1\% = 2\%\).

3. **Total Percentage Error in BMI:**
   The total percentage error in BMI is the sum of the percentage error due to weight and height. So:

   \[
   \text{Total error} = 1\% + 2\% = 3\%
   \]

### Conclusion:
The percentage error in BMI is **3%**.

Would you like further details on this, or do you have any additional questions?

Here are 5 related questions for further exploration:
1. How do you calculate percentage error for other formulas involving multiplication and division?
2. What happens if the errors in weight and height are different percentages?
3. How does squaring or cubing a variable affect percentage error?
4. Can percentage errors ever cancel each other out in certain formulas?
5. How does measurement precision affect error propagation in real-world applications?

**Tip:** When squaring a quantity in an equation, the percentage error gets doubled.

If the errors in weight (W) and height (H) are both 1%, what is the percentage error of BMI?

Learn how to calculate the percentage error in BMI when given a 1% error in both weight (W) and height (H). This problem demonstrates error propagation principles, including how squaring a variable affects error. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation