Mass Bounds 215711

1. **State the problem:** We have an initial mass of chemicals $74$ g (rounded to $2$ significant figures) and a decrease in mass of $6.3$ g (rounded to $2$ significant figures). We want to find the lower and upper bounds of the final mass. 2. **Find the bounds for the initial mass:** Since $74$ is rounded to $2$ significant figures, the bounds are: $$ \text{Lower bound} = 73.5 \text{ g} $$ $$ \text{Upper bound} = 74.5 \text{ g} $$ 3. **Find the bounds for the decrease in mass:** Since $6.3$ is rounded to $2$ significant figures, the bounds are: $$ \text{Lower bound} = 6.25 \text{ g} $$ $$ \text{Upper bound} = 6.35 \text{ g} $$ 4. **Calculate the lower bound of the final mass:** Subtract the upper bound of the decrease from the lower bound of the initial mass: $$ \text{Lower final} = 73.5 - 6.35 = 67.15 \text{ g} $$ 5. **Calculate the upper bound of the final mass:** Subtract the lower bound of the decrease from the upper bound of the initial mass: $$ \text{Upper final} = 74.5 - 6.25 = 68.25 \text{ g} $$ 6. **Final answer:** The mass of the chemicals at the end of the experiment lies between: $$ 67.15 \text{ g and } 68.25 \text{ g} $$ This means the final mass is at least $67.15$ g and at most $68.25$ g.