Mass Tolerance Error
1. **Stating the problem:**
We have a bag of Chama rice with a mass of 25.4 kg. We need to calculate:
(a) the tolerance
(b) the percentage error.
2. **Understanding tolerance:**
Tolerance is the allowable deviation from the stated mass. Usually, tolerance is given or assumed based on the precision of the measurement instrument. Since the problem does not specify tolerance, we assume the tolerance is half of the smallest unit of measurement, which is 0.1 kg here (since the mass is given to one decimal place).
Therefore, tolerance = $\pm 0.05$ kg.
3. **Calculating percentage error:**
Percentage error is calculated as:
$$\text{Percentage error} = \left(\frac{\text{Tolerance}}{\text{Measured value}}\right) \times 100$$
Substitute the values:
$$= \left(\frac{0.05}{25.4}\right) \times 100$$
Calculate the fraction:
$$= 0.0019685 \times 100 = 0.19685\%$$
4. **Final answers:**
(a) Tolerance = $\pm 0.05$ kg
(b) Percentage error = $0.197\%$ (rounded to three decimal places)