1. Chapter 2: Measurement and Problem Solving
The SI System
All units in the SI system are related to the standard unit by a power of 10
The power of 10 is indicated by a prefix
The prefixes are always the same, regardless of the standard unit

2. Common Prefixes in the SI System
Symbol
Decimal
Equivalent
Power of 10
mega- M
1,000,000
Base x 106
kilo- k
1,000
Base x 103
deci- d
0.1
Base x 10-1
centi- c
0.01
Base x 10-2
milli- m
0.001
Base x 10-3
micro-
m or mc
Base x 10-6
nano- n
Base x 10-9

3. Length
= Measure of the two-dimensional distance an object covers
SI unit = meter
About 3½ inches longer than a yard
1 meter = one ten-millionth the distance from the North Pole to the Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of light
Commonly use centimeters (cm)
1 m = 100 cm
1 cm = 0.01 m = 10 mm
1 inch = 2.54 cm (exactly)

4. Mass
= Measure of the amount of matter present in an object
SI unit = kilogram (kg)
about 2 lbs. 3 oz.
Commonly measure mass in grams (g) or milligrams (mg)
1 kg = pounds, 1 lbs. = g
1 kg = 1000 g = 103 g,
1 g = 1000 mg = 103 mg
1 g = kg = 10-3 kg,
1 mg = g = 10-3 g

5. Volume
= Measure of the amount of three-dimensional space occupied
SI unit = cubic meter (m3)
a Derived Unit
Commonly measure solid volume in cubic centimeters (cm3)
1 m3 = 106 cm3
1 cm3 = 10-6 m3 = m3
Commonly measure liquid or gas volume in milliliters (mL)
1 L is slightly larger than 1 quart
1 L = 1 dL3 = 1000 mL = 103 mL
1 mL = L = 10-3 L
1 mL = 1 cm3

6. Common Units and Their Equivalents
Length
1 kilometer (km) =
mile (mi)
1 meter (m)
39.37 inches (in.)
1.094 yards (yd)
1 foot (ft)
30.48 centimeters (cm)
1 inch (in.)
2.54 centimeters (cm) exactly
Mass
1 kilogram (kg) =
2.205 pounds (lb)
1 pound (lb)
grams (g)
1 ounce (oz)
28.35 (g)

7. Common Units and Their Equivalents
Volume
1 liter (L) =
1000 milliliters (mL)
1000 cubic centimeters (cm3)
1.057 quarts (qt)
1 U.S. gallon (gal)
3.785 liters (L)

8. Problem Solving and Dimensional Analysis
Arrange conversion factors so starting unit cancels
Arrange conversion factor so starting unit is on the bottom of the conversion factor
May string conversion factors
So we do not need to know every relationship, as long as we can find something else the beginning and ending units are related to
unit 1
unit 2 x =

9. Dimensional Analysis Exercise 1: Convert 7.8 km to miles
Write down the Given quantity and its unit
Given:
7.8 km
Write down the quantity you want to Find and unit
Find:
? miles
Write down the appropriate Conversion Factors
Conversion Factors:
1 km = mi
Write a Solution Map
Solution
Map:
Follow the Solution Map to Solve the problem
Solution:
Sig. Figs. and Round
Round:
mi = 4.8 mi
Check
Check:
Units & Magnitude are correct km mi

10. Dimensional Analysis Exercise 2: Convert 20.0 lbs to kg
Write down the Given quantity and its unit
Given:
20.0 lbs
Write down the quantity you want to Find and unit
Find:
? kg
Write down the appropriate Conversion Factors
Conversion Factors:
1 kg = pounds
Write a Solution Map
Solution
Map:
Follow the Solution Map to Solve the problem
Solution:
Sig. Figs. and Round
Round:
kg = 9.1 kg
Check
Check:
Units & Magnitude are correct
lbs kg

11. Dimensional Analysis Exercise 3: How many cups of cream is 0.75 L?
Write down the Given quantity and its unit
Given:
0.75 L
Write down the quantity you want to Find and unit
Find:
? cu
Write down the appropriate Conversion Factors
Conversion Factors:
1 L = qt
1 qt = 4 cu
Write a Solution Map
Solution
Map:
Follow the Solution Map to Solve the problem
Solution:
Sig. Figs. and Round
Round:
3.171 cu = 3.2 cu
Check
Check:
Units & Magnitude are correct L qt cu

12. Converting Quantities Involving Units Raised to a Power
Convert Cubic Inches into Cubic Centimeters
Find Relationship Equivalence: 1 in = 2.54 cm
Write Solution Map
in3
cm3
Change Equivalence into Conversion Factors with Starting Units on the Bottom

13. Convert 2,659 cm2 into square meters
Write down the Given quantity and its unit
Given:
2,659 cm2
Write down the quantity you want to Find and unit
Find:
? m2
Write down the appropriate Conversion Factors
Conversion Factors:
1 cm = 0.01 m
Write a Solution Map
Solution
Map:
Follow the Solution Map to Solve the problem
Solution:
Sig. Figs. and Round
Round: m2
Check
Check:
Units & Magnitude are correct
cm2 m2

14. y = 8.38x Volume vs Mass of Brass Mass, g Volume, cm3 20 40 60 80 10020 40 60 80
100
120
140
160
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
Volume, cm3
Mass, g

15. Density
Ratio of mass:volume
Solids = g/cm3
1 cm3 = 1 mL
Liquids = g/mL
Gases = g/L
Volume of a solid can be determined by water displacement – Archimedes Principle
Density : solids > liquids >>> gases
except ice is less dense than liquid water!

16. Density
For equal volumes, denser object has larger mass
For equal masses, denser object has smaller volume
Heating objects causes objects to expand
does not effect their mass!!
How would heating an object effect its density?
In a heterogeneous mixture, the denser object sinks
Why do hot air balloons rise?

17. Density
Solution Maps:
m, V D
m, D V
V, D m

18. Density as a Conversion Factor
The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of g/cm3. What is the volume?
Given: kg
Find: Volume in L
Conversion Factors:
0.752 grams/cm3
1000 grams = 1 kg

19. Density as a Conversion Factor
Exercise:
A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm3?