Significant Figures

Question

The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is the total mass of the box with correct significant figures?

RankGuru · Accepted Answer

1. **Uniform Units**: Convert all measurements to kg.
   - Mass of box: $2.3$ kg.
   - Gold piece 1: $20.15 	ext{ g} = 0.02015$ kg.
   - Gold piece 2: $20.17 	ext{ g} = 0.02017$ kg.
2. **Arithmetic Sum**: $2.3 + 0.02015 + 0.02017 = 2.34032$ kg.
3. **Significant Figures for Addition**: The result of an addition or subtraction should have the same number of **decimal places** as the measurement with the least decimal places.
4. **Identify Constraints**: $2.3$ kg has only **one decimal place** (uncertainty at the tenths place).
5. **Rounding**: Rounding $2.34032$ to one decimal place gives **2.3 kg**.
6. **Physical Interpretation**: The grocer's balance is too coarse to reflect the addition of tiny gold pieces in the final significant figure count.

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