Question

1. perform the following conversions. show your work for each conversion, and box your final answer including the units. list your final answer in float notation or scientific notation.

a. 150 grams = ______ kilograms
b. 20 megawatts = ______ watts
c. 10 milligrams = ______ kilograms
d. 3 nanoseconds = ______ seconds
e. 42 milliseconds = ______ seconds
f. 9 gigajoules = ______ joules
g. 300 deciliters = ______ liters
h. 3 millitorr = ______ torr
i. 20 centimeters = ______ meters
j. 3 kilometers = ______ meters

1. in the nearpod for monday / tuesday i taught you a method of unit conversion that used \conversion factors\. for instance, if i wanted to convert 45 miles per hour to meters per second, i would write out 45 with \miles\ written in the numerator of a fraction with \hour\ underneath as the denominator. then we would write out a conversion factor in parenthesis next to it, and keep adding conversion factors until we got the units we wanted. use this method to convert the following quantities below. make sure to show all of your work and all of the conversion factors that you use. remember there are approximately 1609 meters in a mile.

a. 45 miles per hour = ______ meters per second
b. 30 kilometers per hour = ______ meters per second
c. 5 meters per second = ______ miles per hour
d. 10 meters per second = ______ miles per hour
e. 60 miles per hour = ______ meters per second
f. 80 miles/minute = ______ meters per day
g. 100 liters per hour = ______ gallons per second

Explanation:

Step1: Recall metric - prefix conversion factors

1 kilogram (kg) = 1000 grams (g), so 1 g=$\frac{1}{1000}$ kg = 10^{- 3} kg.
For a. 150 grams to kilograms:
$150\ g\times\frac{1\ kg}{1000\ g}=0.15\ kg$

Step2: Recall Mega - prefix conversion

1 Megawatt (MW)=10^{6} Watts (W).
For b. 20 Megawatts to Watts:
$20\ MW\times\frac{10^{6}\ W}{1\ MW}=2\times10^{7}\ W$

Step3: Recall milli - and kilo - prefix conversion

1 kilogram (kg) = 1000000 milligrams (mg), so 1 mg = 10^{-6} kg.
For c. 10 milligrams to kilograms:
$10\ mg\times\frac{1\ kg}{10^{6}\ mg}=1\times10^{-5}\ kg$

Step4: Recall nano - prefix conversion

1 nanosecond (ns)=10^{-9} seconds (s).
For d. 3 nanoseconds to seconds:
$3\ ns\times\frac{1\ s}{10^{9}\ ns}=3\times10^{-9}\ s$

Step5: Recall milli - prefix conversion

1 millisecond (ms)=10^{-3} seconds (s).
For e. 42 milliseconds to seconds:
$42\ ms\times\frac{1\ s}{10^{3}\ ms}=0.042\ s$

Step6: Recall Giga - prefix conversion

1 Gigajoule (GJ)=10^{9} Joules (J).
For f. 9 Gigajoules to Joules:
$9\ GJ\times\frac{10^{9}\ J}{1\ GJ}=9\times10^{9}\ J$

Step7: Recall deci - prefix conversion

1 liter (L)=10 deciliters (dL), so 1 dL = 0.1 L.
For g. 300 deciliters to liters:
$300\ dL\times\frac{1\ L}{10\ dL}=30\ L$

Step8: Recall milli - prefix conversion

1 millitorr (mTorr)=10^{-3} torr.
For h. 3 millitorr to torr:
$3\ mTorr\times\frac{1\ Torr}{10^{3}\ mTorr}=3\times10^{-3}\ Torr$

Step9: Recall centi - prefix conversion

1 meter (m)=100 centimeters (cm), so 1 cm = 0.01 m.
For i. 20 centimeters to meters:
$20\ cm\times\frac{1\ m}{100\ cm}=0.2\ m$

Step10: Recall kilo - prefix conversion

1 kilometer (km)=1000 meters (m).
For j. 3 kilometers to meters:
$3\ km\times\frac{1000\ m}{1\ km}=3000\ m$

For 11:

Step1: Convert 45 miles per hour to meters per second

1 mile = 1609 meters, 1 hour = 3600 seconds.
$45\frac{miles}{hour}\times\frac{1609\ m}{1\ mile}\times\frac{1\ hour}{3600\ s}\approx20.12\ m/s$

Step2: Convert 30 kilometers per hour to meters per second

1 kilometer = 1000 meters, 1 hour = 3600 seconds.
$30\frac{km}{h}\times\frac{1000\ m}{1\ km}\times\frac{1\ h}{3600\ s}\approx8.33\ m/s$

Step3: Convert 5 meters per second to miles per hour

1 mile = 1609 meters, 1 hour = 3600 seconds.
$5\frac{m}{s}\times\frac{1\ mile}{1609\ m}\times\frac{3600\ s}{1\ h}\approx11.18\ mph$

Step4: Convert 10 meters per second to miles per hour

$10\frac{m}{s}\times\frac{1\ mile}{1609\ m}\times\frac{3600\ s}{1\ h}\approx22.37\ mph$

Step5: Convert 60 miles per hour to meters per second

$60\frac{miles}{hour}\times\frac{1609\ m}{1\ mile}\times\frac{1\ hour}{3600\ s}\approx26.82\ m/s$

Step6: Convert 80 miles/minute to meters per day

1 mile = 1609 meters, 1 day = 24 hours, 1 hour = 60 minutes.
$80\frac{miles}{minute}\times\frac{1609\ m}{1\ mile}\times\frac{60\ minutes}{1\ hour}\times\frac{24\ hours}{1\ day}=1.85\times10^{7}\ m/day$

Step7: Convert 100 liters per hour to gallons per second

1 liter = 0.264172 gallons, 1 hour = 3600 seconds.
$100\frac{L}{h}\times\frac{0.264172\ gal}{1\ L}\times\frac{1\ h}{3600\ s}\approx0.00734\ gal/s$

Answer:

a. 0.15 kg
b. $2\times10^{7}$ W
c. $1\times10^{-5}$ kg
d. $3\times10^{-9}$ s
e. 0.042 s
f. $9\times10^{9}$ J
g. 30 L
h. $3\times10^{-3}$ Torr
i. 0.2 m
j. 3000 m

1. a. $\approx20.12$ m/s

b. $\approx8.33$ m/s
c. $\approx11.18$ mph
d. $\approx22.37$ mph
e. $\approx26.82$ m/s
f. $1.85\times10^{7}$ m/day
g. $\approx0.00734$ gal/s