Ch. 3 Scientific
Measurement
Measurement
 Quantitative
information
 Need a number and a unit (most of time)
 Represents a quantity
 For example: 2 meters



2 is number
Meters is unit
Length is quantity
 Units
compare what is being measured to
a defined measurement standard
SI Measurement
 Le
Systeme International d’Unites : SI
 System of measurement agreed on all
over the world in 1960
 Contains 7 base units
 We
still use some non-SI units
Important SI Base Units
Quantity
Length
Symbol
l
Unit
Abbreviation
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temperature
T
Kelvin
K
Amount
n
mole
mol
Prefixes

Prefixes are added to the base unit names to
represent quantities smaller or larger
M
mega
106
1,000,000
larger
k
kilo
103
1,000
larger
c
centi
10-2
1/100
smaller
m
milli
10-3
1/1000
smaller
μ
micro
10-6
1/1,000,000
smaller
Length
 SI
unit: m
 use cm a lot too
 km is used instead of miles for
highway distances and car speeds in
most countries
Mass
 Measure
of the quantity of matter
 SI unit: kg
 use g a lot too
 mass vs. weight



weight is the measure of gravitational pull on
matter
mass does not depend on gravity
on a new planet, mass would be same but
weight could change
Temperature Conversions
Fahrenheit to Celsius
9
F  C  32
5
5
C  F  32
9
Celsius to Kelvin conversions
+273.15
→
C
K
←
-273.15
Temperature Conversions
Example

What is 32°F in Kelvin?
 freezing point of water!
5
C  (32  32)  0
9
K  0  273.15  273.15
Example

What is 298 K in Fahrenheit?
C  298  273  25 C
o
9

F  (25)  32  77 F
5
Derived SI Units
 come
from combining base units
 combine using multiplication or division
Example:
Area: A = length x width
=mxm
= m2
Volume
 amount
of space occupied by object
 SI: m3 = m x m x m
 use cm3 in lab a lot
 non-SI:
1 liter = 1dm3= 1000cm3
1 liter = 1000 mL
1cm 3= 1mL
Density


ratio of mass to volume
kg
SI:
m

3
mass
Density 
volume
Other units: g/ cm3 or g/ mL
 characteristic property of substance (doesn’t
change with amount ) because as volume
increases, mass also increases
 density usually decreases as T increases
exception: ice is less dense than liquid water so
it floats
Example
A sample of aluminum metal has a mass of
8.4 g. The volume is 3.1 cm3. Find the
density.
Known
Unknown
m = 8.4 g
D=?
V = 3.1 cm3
m
8.4 g
g
D 
 2.7 3
3
V 3.1cm
cm
Dimensional Analysis
Conversion Factors
 ratio
that comes from a statement of
equality between 2 different units
 every conversion factor is equal to 1
Example:
statement of equality
conversion factor
4quarters  1dollar
1dollar
1
4quarters
Conversion Factors
 can
be multiplied by other numbers
without changing the value of the
number
 since you are just multiplying by 1
4quarters
3dollars 
 12quarters
1dollar
Example 1
Convert 5.2 cm to mm
5.2 cm= 5.2 x 10 1mm = 52 mm
 Known: 100 cm = 1 m
1000 mm = 1 m
 Must
use m as an intermediate
1m
1000mm
5.2cm 

 52mm
100cm
1m
Example 2
Convert 0.020 kg to mg
0.020 kg = 0.020 x 10 6 mg= 20,000 mg

Known: 1 kg = 1000 g
1000 mg = 1 g
 Must
use g as an intermediate
1000 g 1000mg
0.020kg 

 20,000mg
1kg
1g
Example 3
Convert 500,000 μg to kg
500,000 μg = 500,000 x 10 -9 kg= 0.0005 kg
 Known: 1,000,000 μg = 1 g
1 kg = 1000 g
 Must
use g as an intermediate
1g
1kg
500,000g 

 0.0005kg
1,000,000g 1000 g
Advanced Conversions

One difficult type of conversion deals with
squared or cubed units
Example

Convert 3 dm 3 to cm3
1dm =10 cm
3 dm 3 = 3 x 10 cm x 10 cm x 10 cm= 3000 cm3
Example

Convert:
2000 cm3 to m3
Known:
100 cm = 1 m
cm3 = cm x cm x cm
m3 = m x m x m
 1m   1m   1m 
3
2000cm  cm  cm 


  0.002m
 100cm   100cm   100cm 
3
OR
 1m 
3
2000cm  

0
.
002
m

 100cm 
3
Advanced Conversions
 Another
difficult type of conversion deals
units that are fractions themselves
 Be
sure convert one unit at a time; don’t
try to do both at once
 Work
on the unit on top first; then work on
the unit on the bottom
Example
Convert 350 g/ mL to kg/L
 Top first
350 g to kg
350 g= 350 x 10 -3 kg= .35 kg
 Bottom part after
1mL to L
1mL= 1x 10 -3 L= 0.001 L
 Result:
350 g/ mL = .35 kg/ 0.001L= 350kg/ L
Combination Example
Convert 7634 mg/m3 to Mg/L

Top
7634 mg= 7634 x 10 -9 Mg= 0.000007634 Mg

Bottom
1m= 10 dm
1 m3= 10 dm x 10 dm x10 dm= 1000 dm 3 = 1000 L

Result:
7634 mg/m3 = 0.000007634 Mg/ 1000 L= 0.000000007634 Mg/L
= 7.634 x 10 -9 Mg/L
Accuracy vs. Precision
 Accuracy-
closeness of measurement to
correct or accepted value
 Precision- closeness of a set of
measurements
Accuracy vs. Precision
Percent Error vs. Percent Difference
 Percent
Error:
 Measures the accuracy of an
experiment
 Can have + or – value
accepted  experimeta l
100%
accepted
Percent Error vs. Percent Difference
 Percent
Difference:
 Used when one isn’t “right”
 Compare two values
 Measures precision
value 1  value 2
average of value 1 and 2
100%
Example
 Measured
density from lab experiment is
1.40 g/mL. The correct density is 1.36
g/mL.
 Find the percent error.
1.36 - 1.40
% error 
100  2.94%
1.36
Example

Two students measured the density of a
substance. Sally got 1.40 g/mL and Bob got 1.36
g/mL.
 Find the percent difference.
1.40 - 1.36
% difference 
100  2.90%
1.40  1.36
2