The mass of each steel bolt is approximately 5g, but there is a variation of ±1.9%. This means that each bolt can have a mass between:

$5g \times (1 - 0.019) = 5g \times 0.981 = 4.905g$ (minimum mass) and $5g \times (1 + 0.019) = 5g \times 1.019 = 5.095g$ (maximum mass).

The total mass of the box is 1kg, or 1000g.

Step 1: Maximum number of bolts

To get the maximum number of bolts, we assume each bolt has the minimum mass of 4.905g: $\text{Number of bolts} = \frac{1000g}{4.905g/bolt} \approx 203.86$ Since we can't have a fraction of a bolt, we round down to 203 bolts.

Step 2: Minimum number of bolts

To get the minimum number of bolts, we assume each bolt has the maximum mass of 5.095g: $\text{Number of bolts} = \frac{1000g}{5.095g/bolt} \approx 196.26$ We round down to 196 bolts.

Conclusion

• The maximum number of bolts is 203.
• The minimum number of bolts is 196.

Would you like a more detailed explanation or clarification?

Here are some related questions:

1. How do you calculate the percentage variation for different mass values?
2. What impact does rounding have in real-world measurements like this?
3. How could Severin measure the exact number of bolts in the box?
4. What are other methods to estimate the mass of individual bolts if only total mass is known?
5. How would changing the percentage variation affect the possible number of bolts?

Tip: Always ensure you understand the range of error or variation when dealing with measurements to avoid underestimating or overestimating values.