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

$1\ m = 100\ cm$, so to convert $83\ cm$ to $m$, divide by 100.
$83\div100 = 0.83\ m$

Step2: Recall conversion factor for volume

$1\ L=1000\ mL$, so to convert $459\ L$ to $mL$, multiply by 1000.
$459\times1000 = 459000\ mL$

Step3: Recall conversion factor for mass (mass - mass unit)

$1\ ng = 1000\ pg$, so to convert $1123\ pg$ to $ng$, divide by 1000.
$1123\div1000 = 1.123\ ng$

Step4: Recall conversion factor for volume (volume - volume unit)

$1\ m^{3}=1000\ L$, so to convert $0.032\ m^{3}$ to $L$, multiply by 1000.
$0.032\times1000 = 32\ L$

Step5: Recall conversion factor for length

$1\ mm = 1000\ \mu m$, so to convert $2.5\ mm$ to $\mu m$, multiply by 1000.
$2.5\times1000 = 2500\ \mu m$

Step6: Recall conversion factor for time

$1\ ns = 1000\ ps$, so $1.2\ ns=1.2\times1000 = 1200\ ps$. Since $1351\ ps>1200\ ps$, $1351\ ps$ is longer.

Step7: Recall conversion factor for pressure

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

Step8: Recall conversion factor for mass

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

Step9: Recall conversion factor for length

$1\ cm = 10\ mm$, so $38.4\ cm = 38.4\times10=384\ mm$. Since $175.6\ mm<384\ mm$, $175.6\ mm$ is shorter.

Step10a: Recall conversion factor for mass

$1\ mg = 0.001\ g$, so $0.7824\ mg=0.7824\times0.001 = 0.0007824\ g$

Step10b: Recall conversion factor for mass

$1\ ng = 1\times10^{-9}\ g$, so $345000\ ng=345000\times1\times10^{-9}=0.000345\ g$

Step10c: Recall conversion factor for mass

$1\ kg = 1000\ g$, so $0.00378\ kg=0.00378\times1000 = 3.78\ g$

Step10d: Recall conversion factor for mass

$1\ \mu g = 1\times10^{- 6}\ g$, so $34981\ \mu g=34981\times1\times10^{-6}=0.034981\ g$

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. $175.6\ mm$

10a. $0.0007824\ g$
10b. $0.000345\ g$
10c. $3.78\ g$
10d. $0.034981\ g$