DIMENSIONAL ANALYSIS CHALLENGE - ANSWERS
1
Measurements and Calculations
How Are Measurements and Calculations Important in the Science of Chemistry?
DIRECTIONS: Solve the following problems as a group. You should show your work (where appropriate)
and cancel all units. We will go over the answers to these problems as a class.
It may be helpful to approach each problem with the following strategy: What are we being asked to do?
What information are we given? How can we use this information to solve the problem? Does our answer
make sense?
1. What units would appear in the answer to a calculation which uses the following sequence of
conversion factors?
quark passel 2 goober parsec speck 2 parsec  speck
x
x
x
x

goober
speck
passel quark 3 passel
quark 2
2. Use your calculator to solve the following. Express your answer in correct scientific notation.
6.02x10 5.02x10 2.4x10 8.5x10 = 235577219.4 or 2.356x10
5.8x10 4.7x10 9.6x10 
23
13
-9
-15
11
7
8
18
3. Using any/all of the following equivalence statements, convert 3 fizzles to frizzles.
4 swizzles = 7 twizzles
2 fizzles = 3 drizzles
4 twizzles = 1 sizzle
10 swizzles = 4 frizzles
2 drizzles = 6 sizzles
3 fizzles x
3 drizzles 6 sizzles 4 twizzles 4 swizzles
4 frizzles
x
x
x
x
 12.34 frizzles
2 fizzles 2 drizzles
1sizzle
7 twizzles 10 swizzles
4. Using your knowledge of English and metric system units convert 20, 000 leagues to meters
1 league = 3 nautical miles
1 nautical mile = 6080 feet
20,000 leagues x
3 nautical miles
6080 feet
1yard
1meter
x
x
x
 111, 192, 392.1 meters
1league
1nautical mile 3 feet 1.0936 yards
Or another way…
20, 000 leagues x
3 nautical miles
6080 feet
1mile
1.6093 km 1000 meters
x
x
x
x
 111, 236, 363.6 meters
1league
1nautical mile 5, 280 feet
1mile
1km
5. How many millimeters would this be?
To convert FROM meters TO millimeters…multiply by 1000…that’s a LOT of millimeters!
6. Express the quantity 452.23x105 in correct scientific notation:
For this problem it may help to convert the “incorrect” form of scientific notation given in the
problem to its “normal” decimal equivalent…
452.23x105 = 45, 223, 000
…then put it in proper scientific notation: 4.5223x107
7. If gasoline costs $3.98 per gallon, how much will it cost to fill up a gas tank that has a volume
of 2.30x102 liters?
This problem requires two steps…first change the 2.30x102 liters TO gallons: (You could also convert
the $3.98 per gallon TO $ per liter)
2.30x10 2 liters x
1gallon
 60.76 gallons
3.7854 liters
-OR-
1gallon
$3.98
$1.05
x

gallon 3.7854 liters Liter
Then, multiply by the cost of gasoline per gallon: (OR multiply the $/L by the size of the tank)
$3.98
$1.05
-OR $241.82
x 2.30x10 2 Liters  $241.50
gallon
Liter
NOTICE that we get (relatively speaking) the same answer either way…my difference is due to
rounding numbers…
60.76 gallons x
8. Convert the speed of 65 miles per hour to m/sec…to km/day
65 miles 1.6093 km 1000m 1hour
1min
x
x
x
x
 29.06 m sec
hour
1mile
1km
60 min 60 sec
65 miles 1.6093 km 24 hours
x
x
 2510.5 km day
hour
1mile
1day
9. If your car gets 26 miles per gallon, how many meters could your car travel on 10 gallons of
fuel?
Similar to question 7…there are a few ways to solve this problem. One way would be to convert the
26 miles/gal to meters/gal then multiply by the amount of fuel (10 gallons):
26 miles 1.6093km 1000m
x
x
 41, 841.8 meters gallon
gallon
1mile
1km
41, 841.8 meters
x 10 gallons  418, 418 meters
gallon
-ORWe could do the multiplying first to get a distance in miles that could be traveled with
those 10 gallons of fuel…then convert miles to meters:
26 miles
x 10 gallons  260 miles
gallon
260 miles x
1.6093 km 1000 m
x
 418, 418 m
1mile
1km
10. If you work 40 hours per week and make $7.50 per hour, how many years will you have to work
to make $1 million?
40 hours 52 weeks $7.50 $15, 600
…now we can use that answer like a conversion factor to answer
x
x

1week
1year
1hr
year
the questions that remains which is…if we make $15,600 per year and we want to make $1million…how
many years will we have to work?
1year
$ 1, 000, 000 x
 64.1 years
$15, 600