CP Chemistry
WS Conversion Factors/Dimensional Analysis
Name_________________
Date___________ Pd. __
Dimensional Analysis (Factor Label)
Using equivalent relationships to obtain unit conversion factors that help you solve a problem.
Unit Conversion Factors – a ratio of two quantities that are equivalent and are used to convert from one
unit to another
1 dollar
100 pennies
100 pennies
1 dollar
To Solve:
1. Write the given number and unit.
2. Set up a conversion factor (fraction used to convert one unit to another)
a. Place the given unit as denominator of conversion factor
b. Place desired unit as numerator
c. Place a “1” in front of the larger unit
d. Determine the number of smaller units needed of make “1” of the larger unit.
3. Cancel units. Solve the problem
Conversion factor:
numerator: what units you want to end with
denominator: what units you start with
Example:
1000 m
1 km
1 km___
1000 m
How many meters are in 35.4 km?
35.4 km x
1000 m
1 km
= 35,400 m
How many km in 54.8 m?
54.8 m x
1 km___
1000 m
= 0.054 km
State the following measured quantities in the units
indicated. Show your work using Factor Label
Method (Dimensional Analysis)!
1) 7.6 cm of magnesium ribbon in millimeters.
1 mile = 5,280 ft
1 inch = 2.54 cm
39.4 inches = 1 meter
3 feet = 1 yard
454 g = 1 lb
946 mL = 1 qt
4 qt = 1 gal
2) 0.012 kg of sulfur in grams.
3) 1500 mL of hydrochloric acid (HCl) in liters.
4) 5, 500, 000 g in kilograms.
5) 1.60 mL of ethanol to microliters.
6) You re throwing a pizza party for 15 people and figure that each person will eat 4 slices.
You call up the pizza place and learn that each pizza will cost $14.78 and it will be cut into
12 slices. How much is the pizza going to cost you? You have $70. Will you have enough
money? Explain.
7) How many milliliters of water will it take to fill a 2 L bottle that already contains 1.87 L of
water?
8) A piece of copper wire is 150 cm long. How long is the wire in millimeters? How many 50
mm segments of wire can be cut from the length?
9) The ladle at an iron foundry can hold 8500 kg of molten iron. 646 metric tons of iron are
needed to make rails. How many ladlefuls of iron will it take to make 646 metric tons of
iron? (1 metric ton = 1000 kg)
Dealing with Two Units
Use conversion factors for each measurement to find the units you need.
Example: If your pace on a treadmill is 65 meters per minute, what is your pace in feet per second?
65 meters x 39.4 inches x 1 foot x 1 min = 3.6 meters/sec
min
1 meter
12 inches 60 s
10) 36 cm/s to miles per hour
11) 4.22 g/cm to lbs/ft
Units Raised to a Power
When converting quantities with units raised to a power, such as cubic centimeters (cm3), the conversion
factor must also be raised to that power, which means raising BOTH the number and unit to that power:
Example: A circle has an area of 28 in2. What is the area in units of square centimeters (cm2)?
Recall conversion factor: 2.54 cm = 1 in
2.54 cm
1 in
28 in2 x
1 in
2.54 cm
(2.54 cm)2
(1 in)2
= 180 cm2
(2 sig figs)
Problems
12) convert 4.3 cm3 to mm3
13) An automobile engine has a displacement (measure of the size of the engine) of 289.7 in3.
What is its displacement in cubic centimeters (cm3)?
Answers:
1) 76 mL
2) 12 g
3) 1.5 L
8) 30 segments
9) 76 ladles
4) 5.5 kg
5) 1600 µL
6) $73.90; no $3.90 short
10) 0.805 mi/h
11) 0.285 lb/ft
12) 4300 mm3
7) 130 mL
13) 4747 cm3