Question

part f. sig fig review: fill in the chart below

1. 21.3 g / 1.3 ml
2. $\frac{8 g}{(1.10 cm\times2.00 cm\times2.0 cm)}$
3. 27.35 cm - 21.2 cm
4. 63.43 l + 34.5 l
5. 0.68 g / 300. cm³
6. 2.25 mm x 3.5 mm
7. 9.341 m + 12.5 m + 4.33 m
8. 56.890 g - 5 g
9. 8.67 g / 3 ml
10. $\frac{3.8 kg}{(1.2 m\times1.35 m\times2 m)}$
11. 0.57 g / 30. cm³
12. 0.0025 g / 0.4 ml

Explanation:

Step1: Calculate 21.3 g/1.3 mL

$21.3\div1.3 = 16.384615$ (Answer without sig - figs). For significant figures, 21.3 has 3 sig - figs and 1.3 has 2 sig - figs. The result should be rounded to 2 sig - figs, so it is 16 g/mL.

Step2: Calculate $\frac{8g}{(1.10cm\times2.00cm\times2.0cm)}$

First, calculate the volume $V = 1.10\times2.00\times2.0=4.4$ $cm^{3}$. Then $\frac{8}{4.4}=1.818182$ (Answer without sig - figs). 8 has 1 sig - fig, 1.10 has 3 sig - figs, 2.00 has 3 sig - figs and 2.0 has 2 sig - figs. The result should be rounded to 1 sig - fig, so it is 2 $g/cm^{3}$.

Step3: Calculate 27.35 cm - 21.2 cm

$27.35−21.2 = 6.15$ (Answer without sig - figs). For subtraction, we consider the decimal place. 21.2 has 1 decimal place, so the result should be rounded to 1 decimal place, so it is 6.2 cm.

Step4: Calculate 63.43 L + 34.5 L

$63.43 + 34.5=97.93$ (Answer without sig - figs). 34.5 has 1 decimal place, so the result should be rounded to 1 decimal place, so it is 97.9 L.

Step5: Calculate 0.68 g/300. $cm^{3}$

$0.68\div300. = 0.00226667$ (Answer without sig - figs). 0.68 has 2 sig - figs and 300. has 3 sig - figs. The result should be rounded to 2 sig - figs, so it is $2.3\times10^{-3}$ $g/cm^{3}$.

Step6: Calculate 2.25 mm×3.5 mm

$2.25\times3.5 = 7.875$ (Answer without sig - figs). 2.25 has 3 sig - figs and 3.5 has 2 sig - figs. The result should be rounded to 2 sig - figs, so it is 7.9 $mm^{2}$.

Step7: Calculate 9.341 m + 12.5 m + 4.33 m

$9.341+12.5 + 4.33=26.171$ (Answer without sig - figs). 12.5 has 1 decimal place, so the result should be rounded to 1 decimal place, so it is 26.2 m.

Step8: Calculate 56.890 g - 5 g

$56.890−5 = 51.890$ (Answer without sig - figs). 5 has no decimal place, so the result should be rounded to no decimal place, so it is 52 g.

Step9: Calculate 8.67 g/3 mL

$8.67\div3 = 2.89$ (Answer without sig - figs). 3 has 1 sig - fig, so the result should be rounded to 1 sig - fig, so it is 3 g/mL.

Step10: Calculate $\frac{3.8kg}{(1.2m\times1.35m\times2m)}$

First, calculate the volume $V = 1.2\times1.35\times2 = 3.24$ $m^{3}$. Then $\frac{3.8}{3.24}=1.17284$ (Answer without sig - figs). 3.8 has 2 sig - figs, 1.2 has 2 sig - figs, 1.35 has 3 sig - figs and 2 has 1 sig - fig. The result should be rounded to 1 sig - fig, so it is 1 $kg/m^{3}$.

Step11: Calculate 0.57 g/30. $cm^{3}$

$0.57\div30. = 0.019$ (Answer without sig - figs). 0.57 has 2 sig - figs and 30. has 2 sig - figs. The result should be rounded to 2 sig - figs, so it is $1.9\times10^{-2}$ $g/cm^{3}$.

Step12: Calculate 0.0025 g/0.4 mL

$0.0025\div0.4 = 0.00625$ (Answer without sig - figs). 0.0025 has 2 sig - figs and 0.4 has 1 sig - fig. The result should be rounded to 1 sig - fig, so it is $6\times10^{-3}$ $g/mL$.

Answer:

Question	Answer without sig figs	Answer with sig figs	Units
2	1.818182	2	g/cm³
3	6.15	6.2	cm
4	97.93	97.9	L
5	0.00226667	$2.3\times10^{-3}$	g/cm³
6	7.875	7.9	mm²
7	26.171	26.2	m
8	51.890	52	g
9	2.89	3	g/mL
10	1.17284	1	kg/m³
11	0.019	$1.9\times10^{-2}$	g/cm³
12	0.00625	$6\times10^{-3}$	g/mL