CW 2.1
Name_________________
Conversion Factors Made Easy

Answer the following mathematical equations
38.5
38.5
38.5
38.5

x
x
x
x
1 = ______
1 x 1 = _______
1 x 1 x 1 = ______
1 x 1 x 1 x 1 = ______
Solve these problems
The same thing = ________
The same thing
If a = b, then a = ______, and b = _______
b
a
One dozen = 12, so
1 m = 10 dm, so
60 sec =1 min, so
1 dozen = _____,
12
1m = ______,
10 dm
60 sec = _____,
1 min
and
12
= _______
1 dozen
and 10 dm = _______
1m
and 1 min = ______
60 sec

We call numbers like

Another example is 55 mph, or 55 miles per hour, or 55 miles . This is a fixed
Hour
definition conversion factor. Word problems often include these in their
“knowns” or “givens.” When working problems be sure to look for these.

Read this word problem and try to fill in the conversion factor list below it
60 sec_ a conversion factor. All conversion factors
1 min
equal one. We might refer to it as 60 seconds per minute.
Mrs. Heck has 7 guests at her house. She is going to make
each guest an omelet. Each omelet takes three eggs. If Mrs.
Heck makes an omelet for each guest, how many cartons of
eggs will it take, if a carton holds twelve eggs?
I omelet
___ guest
3 eggs
__ ______
__ ______
12 eggs
Dimensional Analysis Made Easy 2
Common Conversion Factors
Long Measure - Length
Capacity - Liquid Measure
12 inches
3 feet
5 1/2 yards
40 rods
22 yards
10 chains
8 furlongs
5280 feet
1760 yards
3 miles
4 gills
=
16 fluid oz
=
2 pints
=
4 quarts
=
31 1/2 gallons=
2 barrels
=
=
=
=
=
=
=
=
=
=
=
1
1
1
1
1
1
1
1
1
1
foot
yard
rod
furlong
chain
furlong
mile
mile
mile
league
=
=
=
=
=
=
=
1
1
1
1
1
1
1
square
square
square
rood
acre
acre
square
pint
pint
quart
gallon
barrel
hogshead
Capacity -Dry Measure
2 pints
8 quarts
4 pecks
36 bushels
Square Measure - Area
144 sq.inches
9 sq. feet
30 1/4 sq.yards
40 sq. rods
4 roods
4840 sq. yards
640 acres
1
1
1
1
1
1
foot
yard
rod
mile
=
=
=
=
1
1
1
1
quart
peck
bushel
chaldron
Mariner's Measure
6 feet
= 1 fathom
120 fathoms
= 1 cable length
7 1/3 cable lengths = 1 mile
5,280 ft
= 1 statute mile
6,080.2 feet = 1 nautical mile
Volume - Cubic Measure
1728 cu. ins =
27 cu. feet
=
128 cu. feet =
40 cu. feet
=
2150.42 cu ins=
231 cu inches =
1 cu foot
=

1 cubic foot
1 cubic yard
1 cord wood
1 ton (shipping)
1 standard bush.
1 std US gallon
about 4/5 bushel
Time Measure
60 seconds
60 minutes
24 hours
7 days
28.29.30
or 31 days
365 days
366 days
=
=
=
=
1
1
1
1
minute
hour
day
week
= 1 cal month
= 1 year
= 1 leap year
Using the above conversion chart, write out five different conversion factors,
and then flip them. This is called their reciprocal. Remember, if you flip a
conversion factor over it is still “one.”
Ex: 12 months =
1 year
_1 year__
12 months
Dimensional Analysis Made Easy 3
A Recipe for Solving Problems Using
Dimensional Analysis
Ingredients:
1
chemistry word problem
1
DA track
2-3
good conversion factors
Word Problem:
Mrs. Heck has 7 guests at her house. She is going to make each guest an
omelet. Each omelet takes three eggs. If Mrs. Heck makes an omelet for each guest,
how many cartons of eggs will it take, if a carton holds twelve eggs?
Directions:
1. Draw a Dimensional Analysis (DA) track.
a. Draw a straight line with an equal sign at the end.
=
b. Place a “?” followed by the units requested for the answer to the word
problem, to the right of the “=” sign.
= ? cartons
c. Place the “known” quantity that determines the outcome to the word
problem on the left-top of the DA track, and draw a vertical line.
7 guests
= ? cartons
d. Insert conversion factors that will make all the units cancel except the unit
you’re looking for. Draw vertical lines to separate factors.
7 guests
1 omelet
1 guest
3 eggs
1 omelet
1 carton
12 eggs
= ? cartons
e. Draw through the units that cancel (ex: guest cancels guest, eggs cancel
eggs). Multiply the numbers left in the numerator and the denominator, and
divide the numerator by the denominator to get the final answer.
7 guests
1 omelet
1 guest
3 eggs
1 omelet
1 carton
12 eggs
= ? cartons
(7 x 1 x 3 x 1)/(1 x 1 x 12) = 1.75 cartons Answer
Dimensional Analysis Made Easy 4

Work the following problems using the DA track recipe
EX: How many seconds in 35 minutes?
= ? seconds
35 mins
35 mins
= ? seconds
60 sec
1 min
= ? seconds
(35 x 60 sec)/1 = 2100 sec

You will only draw one DA track when you work your problems. The example
above has three DA tracks only to help illustrate the process.

Problems
1. How many hours are in six days?
2. How many miles in 2640 yards?
3. What is the cost of three shirts, if a box containing 12 shirts cost $27.00?
4. How far will a car travel in 10 seconds if it is going 60 mph?
5. If solution A weighs 22 grams, and its density is 6 grams/liter, how many liters
of solution A do you have?