Question

1-4 practice problems
solve each of the following problems as directed. show all your work. use the correct abbreviation for each unit.

1. convert 83 cm into meters.
2. convert 459 l into milliliters.
3. express 1123 pg in nanograms.
4. express 0.032 m³ in liters.
5. express 2.5 mm in micrometers.
6. which is the longer amount of time, 1351 ps or 1.2 ns?
7. which is the larger pressure, 232.1 kpa or 125,487 pa?
8. which is the smaller mass, 285.0 cg or 23.78 dg?
9. which is the shorter length, 175.6 mm or 38.4 cm?
10. convert the following masses into grams.

a. 0.7824 mg
b. 345,000 ng
c. 0.00378 kg
d. 34,981 μg

Explanation:

Step1: Recall conversion factor for length (cm to m)

We know that 1 m = 100 cm, so to convert cm to m, we divide by 100. For 83 cm, the conversion is $83\div100 = 0.83$ m.

Step2: Recall conversion factor for volume (L to mL)

Since 1 L = 1000 mL, for 459 L, the conversion is $459\times1000=459000$ mL.

Step3: Recall conversion factor for mass (pg to ng)

As 1 ng = 1000 pg, for 1123 pg, the conversion is $1123\div1000 = 1.123$ ng.

Step4: Recall conversion factor for volume ($m^{3}$ to L)

Given 1 $m^{3}$ = 1000 L, for 0.032 $m^{3}$, the conversion is $0.032\times1000 = 32$ L.

Step5: Recall conversion factor for length (mm to $\mu$m)

Since 1 mm = 1000 $\mu$m, for 2.5 mm, the conversion is $2.5\times1000=2500$ $\mu$m.

Step6: Recall conversion factor for time (ps to ns)

We know that 1 ns = 1000 ps, so 1351 ps = $1351\div1000=1.351$ ns. Since 1.351 ns > 1.2 ns, 1351 ps is the longer - time amount.

Step7: Recall conversion factor for pressure (kPa to Pa)

As 1 kPa = 1000 Pa, 232.1 kPa = $232.1\times1000 = 232100$ Pa. Since 232100 Pa>125487 Pa, 232.1 kPa is the larger pressure.

Step8: Recall conversion factor for mass (cg to g and dg to g)

1 cg = 0.01 g and 1 dg = 0.1 g. So 285.0 cg=$285.0\times0.01 = 2.85$ g and 23.78 dg=$23.78\times0.1 = 2.378$ g. Since 2.378 g < 2.85 g, 23.78 dg is the smaller mass.

Step9: Recall conversion factor for length (mm to cm)

Since 1 cm = 10 mm, 175.6 mm = $175.6\div10 = 17.56$ cm. Since 17.56 cm < 38.4 cm, 175.6 mm is the shorter length.

Step10: Recall conversion factors for mass (mg to g, ng to g, kg to g, $\mu$g to g)

a. 1 mg = 0.001 g, so 0.7824 mg = $0.7824\times0.001=7.824\times10^{-4}$ g.
b. 1 ng = $10^{-9}$ g, so 345000 ng = $345000\times10^{-9}=3.45\times10^{-4}$ g.
c. 1 kg = 1000 g, so 0.00378 kg = $0.00378\times1000 = 3.78$ g.
d. 1 $\mu$g = $10^{- 6}$ g, so 34981 $\mu$g = $34981\times10^{-6}=0.034981$ g.

Answer:

1. 0.83 m
2. 459000 mL
3. 1.123 ng
4. 32 L
5. 2500 $\mu$m
6. 1351 ps
7. 232.1 kPa
8. 23.78 dg
9. 175.6 mm
10. a. $7.824\times10^{-4}$ g

b. $3.45\times10^{-4}$ g
c. 3.78 g
d. 0.034981 g