The relative error in a measurement is calculated as the ratio of the absolute uncertainty (smallest division of the scale) to the measured value, multiplied by 100 to convert it to a percentage.

Here’s how to calculate it:

1. Absolute Uncertainty: This is the smallest division of the scale, which is $18.6 \, \text{g}$.
2. Measured Value: The weight of the apples, which is $5.0 \, \text{kg}$ or $5000 \, \text{g}$.
3. Relative Error Calculation:

$\text{Relative Error} = \left( \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \right) \times 100$

Substitute the values:

$\text{Relative Error} = \left( \frac{18.6}{5000} \right) \times 100$

$\text{Relative Error} = 0.372\%$

Answer:

The relative error in this weight measurement is 0.372%.

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

---

Related Questions:

1. How would the relative error change if the apples weighed only 2.5 kg?
2. What would be the relative error if the smallest division of the scale were 10 g?
3. Why is relative error important in measurement?
4. How can the precision of the scale affect the accuracy of the measured weight?
5. How is absolute error different from relative error?

Tip:

Always check the units of measurement to ensure they align across your calculation, especially when dealing with relative errors.