1. **Problem statement:** Calculate each expression and record the result to the correct degree of precision. 2. **Important rules:** - When multiplying or dividing, the result should have the same number of significant figures as the factor with the fewest significant figures. - For addition or subtraction, the result should have the same number of decimal places as the term with the fewest decimal places. 3. **Calculations:** **a)** $(12.6\,m)(4.4\,m)$ - $12.6$ has 3 significant figures. - $4.4$ has 2 significant figures. - Multiply: $12.6 \times 4.4 = 55.44$ - Round to 2 significant figures: $55$ (since 2 sig figs is the least) - **Answer:** $55\,m^2$ **b)** $\frac{315\,km}{1.4\,h}$ - $315$ has 3 significant figures. - $1.4$ has 2 significant figures. - Divide: $\frac{315}{1.4} = 225$ - Round to 2 significant figures: $2.3 \times 10^{2}$ or $230$ (2 sig figs) - **Answer:** $230\,km/h$ **c)** $(14.5\,cm)(14.5\,cm)(5)$ - $14.5$ has 3 significant figures. - $5$ is an exact count (assumed exact, so no sig fig limit). - Multiply: $14.5 \times 14.5 = 210.25$ - Then $210.25 \times 5 = 1051.25$ - Round to 3 significant figures: $1050$ - **Answer:** $1050\,cm^2$ **d)** $(4.5\,cm)(2.25\,cm)(10.6\,cm)$ - $4.5$ has 2 significant figures. - $2.25$ has 3 significant figures. - $10.6$ has 3 significant figures. - Multiply: $4.5 \times 2.25 = 10.125$ - Then $10.125 \times 10.6 = 107.325$ - Round to 2 significant figures: $110$ - **Answer:** $110\,cm^3$