Question

part c. multiplication and division: calculate the following problems. express your answer to the correct sig figs. include units!! objective: express an answer to the correct number of sig figs when multiplying or dividing. 1) 1.90 g/3 ml 2) 2 cm x 2.5 cm 3) 4.0 mm x 4.00 mm x 4.00 mm 4) 5.70 g/0.05 cm³ 5) 0.340 cm x 0.30 cm 6) 2.4 mm x 3.00 mm 7) 56.9 g / (2.0 cm x 3.01 cm x 1.92 cm) 8) 5600 g / (30.0 cm x 32 cm x 31 cm) 9) 600. g/2 ml 10) 450. g / (2.1 cm x 2.1 cm x 2.1 cm)

Explanation:

Step1: Calculate 1.90 g/3 mL

When dividing, the result should have the same number of significant - figures as the number with the fewest significant - figures in the values used in the calculation. 3 has 1 significant - figure. $1.90\div3\approx0.6333\cdots$. Rounding to 1 significant - figure gives $0.6\ g/mL$.

Step2: Calculate 2 cm×2.5 cm

$2\times2.5 = 5.0\ cm^{2}$. 2 has 1 significant - figure and 2.5 has 2 significant - figures. We round to 1 significant - figure, so the answer is $5\ cm^{2}$.

Step3: Calculate 4.0 mm×4.00 mm×4.00 mm

$4.0\times4.00\times4.00=64.000\ mm^{3}$. 4.0 has 2 significant - figures, 4.00 has 3 significant - figures. We round to 2 significant - figures, so the answer is $64\ mm^{3}$.

Step4: Calculate 5.70 g/0.05 cm³

$5.70\div0.05 = 114\ g/cm^{3}$. 0.05 has 1 significant - figure. Rounding to 1 significant - figure gives $100\ g/cm^{3}$.

Step5: Calculate 0.340 cm×0.30 cm

$0.340\times0.30 = 0.102\ cm^{2}$. 0.340 has 3 significant - figures and 0.30 has 2 significant - figures. We round to 2 significant - figures, so the answer is $0.10\ cm^{2}$.

Step6: Calculate 2.4 mm×3.00 mm

$2.4\times3.00 = 7.20\ mm^{2}$. 2.4 has 2 significant - figures and 3.00 has 3 significant - figures. We round to 2 significant - figures, so the answer is $7.2\ mm^{2}$.

Step7: Calculate $\frac{56.9\ g}{2.0\ cm\times3.01\ cm\times1.92\ cm}$

First, calculate the volume: $V = 2.0\times3.01\times1.92=11.5584\ cm^{3}$. Then, $\frac{56.9}{11.5584}\approx4.92\ g/cm^{3}$. 2.0 has 2 significant - figures. Rounding to 2 significant - figures gives $4.9\ g/cm^{3}$.

Step8: Calculate $\frac{5600\ g}{30.0\ cm\times32\ cm\times31\ cm}$

First, calculate the volume: $V = 30.0\times32\times31 = 29760\ cm^{3}$. Then, $\frac{5600}{29760}\approx0.188\ g/cm^{3}$. 32 and 31 have 2 significant - figures. Rounding to 2 significant - figures gives $0.19\ g/cm^{3}$.

Step9: Calculate 600. g/2 mL

$600\div2 = 300\ g/mL$. 2 has 1 significant - figure. Rounding to 1 significant - figure gives $300\ g/mL$.

Step10: Calculate $\frac{450\ g}{2.1\ cm\times2.1\ cm\times2.1\ cm}$

First, calculate the volume: $V=(2.1)^{3}=9.261\ cm^{3}$. Then, $\frac{450}{9.261}\approx48.6\ g/cm^{3}$. 2.1 has 2 significant - figures. Rounding to 2 significant - figures gives $49\ g/cm^{3}$.

Answer:

1. $0.6\ g/mL$
2. $5\ cm^{2}$
3. $64\ mm^{3}$
4. $100\ g/cm^{3}$
5. $0.10\ cm^{2}$
6. $7.2\ mm^{2}$
7. $4.9\ g/cm^{3}$
8. $0.19\ g/cm^{3}$
9. $300\ g/mL$
10. $49\ g/cm^{3}$