To find the relative error between the actual height and the measured height, follow these steps:

Formula for Relative Error:

$\text{Relative Error} = \frac{\text{Measured Value} - \text{Actual Value}}{\text{Actual Value}}$

Step-by-Step Calculation:

1. Actual Value (friend's actual height) = 165 cm = 1.65 m (convert to meters)
2. Measured Value (your measurement) = 1.68 m

Now, plug in the values:

$\text{Relative Error} = \frac{1.68 \, \text{m} - 1.65 \, \text{m}}{1.65 \, \text{m}} = \frac{0.03 \, \text{m}}{1.65 \, \text{m}}$

$\text{Relative Error} \approx 0.01818$

Rounding this to one significant figure, the relative error is approximately:

$\text{Relative Error} \approx 0.02$

Thus, the relative error is about 0.02 or 2%.

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Do you want further details or have any questions about this calculation? Here are some related questions to expand your understanding:

1. How is absolute error different from relative error?
2. Why do we round to one significant figure in error calculations?
3. What is the importance of relative error in measurements?
4. How would the result change if you measured your friend's height as 1.70 m?
5. Can relative error be negative, and what does that indicate?

Tip: Always use the same units when calculating errors to avoid confusion and ensure accuracy!