CHAPTER 1
UNITS OF MEASUREMENT
Objectives
1. To understand the use of the SI system of measurement
2. To convert from one system of measurement to another
3. To understand the use of the factor label method
4. To understand the use of significant figures
5. To interconvert temperatures in Fahrenheit, Celsius, Kelvin and Rankine Scales
6. To perform density calculations
SYSTEMS OF MEASUREMENT
A system of measurement is a collection of units of measurement and rules relating them to
each other.
Examples of systems of measurement in modern use include the Metric System, the Imperial System,
and the United States Customary Units.
The Metric System is an internationally agreed decimal system of measurement.
The metric system is now often used as a synonym for “SI” or the “System International”, the official
system of measurement in almost every country in the world.
The Imperial System develop from what were first known as English Units, as did the related system of
United States customary units.
For measuring length, the U.S. Customary System uses the inch, foot, yard and mile, which are the only
four customary length measurements in every day used.
Therefore, there are two main systems of measurement in the world.
The Metric (or Decimal) System, and
the US Standard System.
TABLE 1.1 COMMON PHYSICAL QUANTITIES AND STANDARD UNITS OF
MEASUREMENT
A. FUNDAMENTAL QUANTTITIES
QUANTITY UNIT SYMBOL
Length Meter m
Mass Kilogram kg
Time Second s
Electric Current Ampere A
Temperature Kelvin K
Amount of Substance Mole mol
Luminous Intensity Candela cd
B. DERIVED QUANTITIES UNIT SYMBOL
Area square meter m2
Volume cubic meter m3
Density kilogram per cubic meter kg/m3
Speed/Velocity meter per second m/s
Acceleration meter per second squared m/s2
Force/Weight Newton N
Pressure Pascal Pa
Work Joule J
Power Watt W
TABLE 1.2 SOME PREFIXES USED IN THE SI SYSTEM
PREFIX ABBREVIATION DECIMAL EXPONENTIAL
EXPRESSION EXPRESSION
mega M 1,000,000 106
kilo k 1,000 103
hekto h 100 102
deka da 10 101
- - 1 100
deci d 0.1 10-1
centi c 0.01 10-2
milli m 0.001 10-3
micro mc or µ 0.000001 10-6
nano n 0.000000001 10-9
TABLE 1.3 METRIC CONVERSIONS
Mass ( Weight ) Length Volume
1 g = 1000 mg 1 m = 1000 mm 1 L = 1000 mL
1 g = 100 cg 1 m = 100 cm 1 L = 100 cL
1 g = 10 dg 1 m = 10 dm 1 L = 10 dL
1 kg = 1000 g 1 km = 1000 m 1 Kl = 1000 L
FACTOR LABEL METHOD
12 in = 1 ft
3 ft = 1 yd
1760 yd = 1 mi
2.54 cm = 1 in
454 g =1 lb
2.2 lb =1 kg
` 1. 06 qt = 1 L
EXERCISE 1.1
1. Complete the equation for each metric relationship.
a. 1 liter = _____ mL b. 1 cm = _____ m
2. Convert 512 mg to kg.
3. Convert 24 days, 54 hours and 56 minutes to second.
Answer:
1 minute = 60 seconds
1 hour = 60 minutes
1day = 24 hours
56minutes x 60sec = 3,360sec
60minutes x 60sec = 3,600sec x 54hours = 194,400
24days x 86,400sec = 2,073,600
TOTAL OF SECONDS = 2, 271,360
SCIENTIFIC NOTATION
- Uses of powers of 10 to provide an easier way of writing large and small numbers.
TABLE 1.4 POWERS OF TEN
EXPONENTIAL NUMBER ORDINARY NUMBER
106 1 000 000
103 1 000
102 1 00
101 10
100 1
10-1 0.1
10-2 0.01
10-3 0.001
10-6 0.000001
EXERCISE 1.2
1. Write the following as common numbers.
6.2 x 102
8.45 x 105
1.27 x 10-2
3.5 x 10-9
6.02 x 10-5
3.846 x 102
2. Write the following as exponential numbers.
4 000
604
0.00037
0.0000913
6 780 000
3. Perform the following mathematical operation. Give the answer with the correct number of
significant figures.
11.73 g + 6.8 g + 120 g = _____________
150 mL – 6.8 mL = __________________
2.6 cm x 5.2 cm x 11.1 cm = ___________
8.238 g ÷ 0.92 mL
SIGNIFICANT FIGURES (see attached files)
TEMPERATURE SCALES
-Is a measure of the availability of heat or cold or, in simpler terms, of hot or cold a substance is.
-it can be measured by means of a thermometer.
The four temperature scales for measuring temperature are the:
1. Celsius or Centigrade ( oC )- Anders Celsius
Swedish Astronomer
Freezing point – 0oC
Boiling point – 100oC
o
C = 5/9 ( oF – 32)
Exercise 1.2a
Change 80.0 oC to oF.
2. Fahrenheit ( OF )- Daniel Gabriel Fahrenheit
German Physicist
Freezing point – 32oF
Boiling point - 212oF
o
F = 9/5OC + 32
Exercise 1.2b
Change 50oF to oC.
3. Kelvin ( K ) – William Thomson a.k.a Lord Kelvin
British Inventor
Freezing point – 273.15 K
Boiling point – 373.15 K
K = oC + 273.15
Exercise 1.2c
Change 37oC to K.
4. Rankine (oR) – William John Macquorn Rankine
Scottish Engineer and Physicist
Freezing point – 491.67 oR
Boiling point – 671.67 oR
o
R = oF + 459.67
Exercise 1.2d
Change 412oF to oR.
DENSITY
The density of an object helps to characterize it physically and is determined by dividing its mass
(or weight) by its volume. Density can be expressed by the formula
D=M
V
WHERE:
D = density
M = mass
V = volume
Density must have units of mass per unit volume such as g/mL, g/cm 3, lb/ft3 or mg/L.
Try to use conversion factors in solving some problems concerning density.
Exercise 1.3
1. What is the density of the mercury in a thermometer if 31.2 g of it occupies 2.29 mL?
2. Alcohol has a density of 0.80 g/mL. How much will 100 mL of it weigh?
3. A car radiator contains 8.0 L of antifreeze (ethylene glycol). If the density of ethylene glycol
is 1.12 g/mL, how many grams of antifreeze are in the radiator?
4. A solid material has a density of 5 g/mL. What is the volume in litres of 100 g of the
material?
