2. Metrics- Unit Conversions
Factor Label Method
1. Write the given number and unit. (Convert 12 cm to meters.)
2. Set up a conversion
(1 m = 100 cm)
a. Place the given unit as denominator of conversion factor.
1) Conversion factors are simple ratios.
b. Place desired unit as numerator.
c. Place a “1” in front of the larger unit. (m vs. cm)
d. Determine the number of smaller units needed to make “1” of the larger unit. Place it with the applicable unit.
3. Cancel units. Solve the problem. 1 m
12 cm
= 0.12 m X
100 cm

3. Dimensional Analysis Factor Label Method
The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out.
This line represents multiplication.
cm3 g = g g 1
cm3
This line represents division.

4. Dimensional Analysis 1 in = 2.54 cm = 1 2.54 cm 2.54 cm 1 in = 2.54 cm
Lining up conversion factors (What is a conversion factor):
= 1
1 in = 2.54 cm
2.54 cm cm
1 =
1 in = 2.54 cm
1 in in

5. Dimensional Analysis 3. Cancel units. Solve the problem.
Factor Label Method
1. Write the given number and unit.
Convert 24.2 inches to centimeters.
2. Set up a conversion factor.
1 inch = 2.54 cm
a. Place the given unit as denominator of conversion factor.
1) Conversion factors are simple ratios.
b. Place desired unit as numerator.
c. Place the applicable values with the corresponding units.
3. Cancel units. Solve the problem.
2.54
_______ cm
24.2 in. X =
61.5 cm 1
in.

6. B. Dimensional Analysis
How many milliliters are in 1.00 quart of milk? qt mL
1.00 qt
1 L
1.057 qt
1000 mL
1 L
= 946 mL 

7. B. Dimensional Analysis
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb
cm3
1.5 lb
1 kg
2.2 lb
1000 g
1 kg
1 cm3
19.3 g
= 35 cm3

8. B. Dimensional Analysis
How many liters of water would fill a container that measures 75.0 in3?
in3 L
75.0 in3
(2.54 cm)3
(1 in)3
1 L
1000 cm3
= 1.23 L

9. B. Dimensional Analysis
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in
8.0 cm
1 in
2.54 cm
= 3.2 in

10. B. Dimensional Analysis
6) Taft football needs 550 cm for a 1st down. How many yards is this? cm yd
550 cm
1 in
2.54 cm
1 ft
12 in
1 yd
3 ft
= 6.0 yd

11. B. Dimensional Analysis
7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? cm
pieces
1.3 m
100 cm
1 m
1 piece
1.5 cm
= 86 pieces

12. M V D = C. Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L
Combination of base units.
Volume (m3 or cm3)
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L
D = M V
Density (kg/m3 or g/cm3)
mass per volume

13. D. Density
Mass (g)
Volume (cm3)

14. Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate