Chapter 2: Measurement
Units of Measurement
• SI units
– based on the International System of Units
• Base unit
– a defined unit based on an object or event in
the physical world
– Important Base Units to Know:
•
•
•
•
Time (second, s)
Length (meter, m)
Mass (kilogram, kg)
Volume (liter, L)
Temperature (Kelvin, K)
Density (grams/centimeter3, g/cm3)
Derived Units
Density and Volume are derived units
meaning that they are combined units
Ex. The volume of a block of wood can be
determined by finding L x W x H 
therefore the units would be cm x cm x cm
or cm3
Ex. Density is mass divided by volume or
g/cm3
Prefixes (p. 26)
Prefix
Symbol
Factor
Scientific
Notation
Example
Giga
G
1000000000
109
gigameter (Gm)
Mega
M
1000000
106
megagram (Mg)
Kilo
k
1000
103
kilometer(km)
Deci
d
1/10
10-1
deciliter (dL)
Centi
c
1/100
10-2
centimeter (cm)
Milli
m
1/1000
10-3
milligram (mg)
Micro
µ
1/1000000
10-6
microgram (µg)
Nano
n
1/000000000
10-9
nanometer (nm)
pico
p
1/000000000000
10-12
picometer (pm)
DENSITY
Density = mass
volume
Regular objects  simply find the mass by
using a balance and then find volume by
measuring length, width, and height (plug
and chug)
What about irregularly shaped objects?
Density of Irregularly
shaped objects
• Measure the mass by using a balance
• How do you find volume?
– WATER DISPLACEMENT METHOD
• Fill a graduated cylinder with certain amount of water (30mL)
• Slowly lower object into the graduated cylinder and measure
the change in water level.
• Ex. Suppose cylinder plus object has a volume of 32 mL
– The change in volume is 2 mL therefore the volume of the
object is 2 mL
Scientific Notation
• Expresses numbers as a multiple of two
factors
– A number between 1 and 10
– A ten raised to a power or exponent
Ex.
5.0 x 103  5000
Calculations with Scientific Notation
• Addition and Subtraction- exponents must be the
same so you will rewrite the number and then perform
operation
4x102 + 5x103 = 4x102 + 50x102 = 54 x 102 or 5.4 x 103
• Multiplication- exponents do not have to equal instead
perform operation on the factors and then add exponents
(3 x 102) x (4 x 105) = 12 x 107 or 1.2 x 10 8
• Division- exponents do not have to be the same instead
perform operation on the factors and then subtract
exponents
(1.5 x 105) / (3x103)= 0.5x102 or 5x101
Accuracy in Measurement
• You cannot be more accurate than the
instrument in which you use to measure
• Ex. A bathroom scale measures pounds
to the 1/10. Will you ever be able to
determine your weight to the 1/1000 with
this particular scale?
NO
Precision of Calculated Results
• calculated results are never more reliable than
the measurements they are built from
• Multi-step calculations: never round intermediate
results!
• General rules on rounding:
– If it ends in 4 or below, round down to nearest whole
number
52.63  52.6
– If it ends in 5 or up, round up to nearest whole
number
52.67  52.7
Uncertainty in Measurements
• Making a measurement involves comparison with a unit
or a scale of units
– It is important to read between the lines
– the digit read between the lines is always uncertain
– convention: read to 1/10 of the distance between the smallest
scale divisions
• Significant Figures
– definition: all digits up to and including the first uncertain digit
– the more significant digits, the more reproducible the
measurement is.
– counts and defined numbers are exact- they have no uncertain
digits!
Rules for Significant Figures
• 1. All digits are significant except for zeros at the
beginning of the number and possibly terminal zeros.
• 2. Terminal zeros to the right of the decimal point are
significant
• 3. Terminal zeros in a number without an explicit decimal
point may or may not be significant. If doubt, write in
scientific notation and then do significant figures.
• 4. When multiplying or dividing, give as many significant
figures in the answer as there are in the measurement
with the least number of significant figures.
• 5. When adding or subtracting measured quantities, give
the same number of decimal places in the answer as
there are in the measurement with the least number of
decimal places.
Examples of the Rules
• Rule 1 example: 9.12 cm, 0.912 cm, and
0.00912 all have 3 sig fig
• Rule 2 example: 9.000 cm, 9.100 cm, and 900.0
cm all have 4 sig fig
• Rule 3 example: 900cm could have 1, 2, or 3 sig
fig. If it was 900., then it would be 3. So, write it
in sci. notation 9.00x102; therefore, 3 sig fig.
• Rule 4 example: 4.1 x 5. =20.5=2. x101
• Rule 5 example: 184.2 +2.324 = 186.5
Conversions Between Units
• Use Factor Label Method aka Dimensional
Analysis
• Must know relationships among units
• These relationships are called conversion
factors
Ex. 1000 mm = 1 m
Common Factors
1km=1000m
1hm=100m
1dam=10m
1m=1 m
1m=10dm
1m=100cm
1m=1000mm
kilometers to meters
hectometers to meters
decameters to meters
base
meter to decimeter
meter to centimeter
meter to millimeter
** substitute any metric base in place such as liter
Common Factors
•
•
•
•
•
•
•
•
•
•
•
•
Tera = 1012
Giga = 109
Mega = 106
Kilo = 103
Hecto = 102
Deca = 101
Deci = 10-1
Centi = 10-2
Milli = 10-3
Micro = 10-6
Nano = 10-9
Pico = 10-12
Symbol: T
Symbol: G
Symbol: M
Symbol: k
Symbol: h
Symbol: da
Symbol: d
Symbol: c
Symbol: m
Symbol: µ
Symbol: n
Symbol: p
How to Convert
EXAMPLE:
4.5 m = _________hm
Xhm = 4.5 m
x 1hm = 0.045 hm or 4.5x10-2 hm
100m
225 cm =________ mm
Xmm = 225cm x 10 mm = 2250 mm or 2.25 x 103 mm
1 cm
Conversion factor is in red
Temperature Conversions
REMEMBER: Kelvin is SI base unit for
temperature
Celsius  Kelvin
K= oC+ 273.15
Fahrenheit  Celsius
oF=(1.8 x oC) +32
Fahrenheit  Celsius  Kelvin