Chapter 3
Scientific
Measurement
Measurements

2 types:

Qualitative measurements (words)
Heavy, hot, or long



Quantitative measurements (#’s) & depend on:
1) Reliability of measuring instrument
2) Care w/ which it’s read – determined by YOU!
Scientific Notation
 Coefficient raised to power 10

(ex. 1.3 x 107)
 Review: Textbook pages R56 & R57
Accuracy, Precision, and Error




Necessary for reliable lab measurements
Accuracy – how close measurement is to
true value
Precision – how close measurements to each
other
Reproducible
 For #’s w/ decimal pt……… decimal place
right-most digit is in
 134.90
 0.0157
Accuracy, Precision, and Error
For #’s w/o decimal pt…...rightmost non-zero #
34200
120390
Precision and Accuracy
Accuracy, Precision, and Error
 Accepted
value – based on
reliable references (Density Table
page 90)
 Experimental
in lab
value - measured
NFL Flyovers 4:53
Accuracy, Precision, and Error

Error = accepted value – experimental value
can be + or 
Percent error = absolute value of error
divided by accepted value, & multiplied by
100%
| error |
x 100%
% error =
accepted value
Significant Figures in Measurements
 Significant
figures all known
digits + one estimated digit
 Measurements must be recorded to
correct # sig figs
Figure 3.5 Significant Figures - Page 67
Which measurement is the best?
What is the
measured value?
What is the
measured value?
What is the
measured value?
Rules for Counting Sig Figs
Non-zeros always count as sig
figs:
3456 has
4 sig figs
Rules for Counting Sig Figs
Zeros
Leading zeroes do
sig figs:
not count as
0.0486 has
3 sig figs
Rules for Counting Sig Figs
Zeros
Captive zeroes always count as
sig figs:
16.07 has
4 sig figs
Rules for Counting Sig Figs
Zeros
Trailing zeros significant only
w/
written decimal point:
9.300 has
4 sig figs
Rules for Counting Sig Figs
Two special situations have
unlimited # sig figs:
1. Counted items
a) 23 people, or 425 thumbtacks
2. Exactly defined quantities
b) 60 minutes = 1 hour
Big Sig Fig Gig (2:27) – Mark Rosengarten
Sig Fig Practice #1
How many significant figures in the following?
1.0070 m  5 sig figs
17.10 kg  4 sig figs
100,890 L  5 sig figs
3.29 x 103 s  3 sig figs
These all come
from some
measurements
0.0054 cm  2 sig figs
3,200,000 mL  2 sig figs
5 dogs  unlimited
This is a
counted value
Sig Figs in Calculations
 answer
cannot be more precise than
least precise measurement.
 Sometimes, calculated values need
rounded off
Rounding Calculated Answers
 Rounding
Decide how many sig figs needed
Round to that many digits, counting from
the left
Is next digit less than 5? Drop it.
 Is next digit 5+? Add 1
- Page 69
Be sure to answer the
question completely!
Rounding Calculated Answers
 Addition
and Subtraction
answer rounded to same #
decimal places as least #
decimal places in problem
- Page 70
Rounding Calculated Answers
 Multiplication
and Division
answer rounded to same # of sig
figs as least # of sig figs in
problem
- Page 71
Rules for Sig Figs in Mathematical
Operations
•
Multiplication and Division: # sig
figs in result = # in least precise
measurement used in calculation.
• 6.38
x 2.0 =
• 12.76  13 (2 sig figs)
Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g x 2.87 mL
2.9561 g/mL
2.96 g/mL
Rules for Sig Figs in Mathematical
Operations
•
Addition and Subtraction: # decimal
places in result = # decimal places in least
precise measurement.
• 6.8
+ 11.934 =
• 18.734  18.7 (3 sig figs)
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
*Note the zero that has been added.
International System of Units
p. 73
 Measurements
depend on units
 The standards of measurement of
science is Metric System
Why science uses the metrics 2:30
International System of Units
 Metric
system now revised &
named International System of
Units (SI), (1960)
 multiples of 10
5
common base units in
chemistry

meter, kilogram, kelvin, second
& mole
Nature of Measurements
Measurement - quantitative observation 2 parts:
•
Part 1 – number
 Part 2 - unit


Examples:
22 grams
 3.55 x 103 moles

International System of Units
 Sometimes, non-SI
units used
Liter, Celsius, calorie
 Derived units
joining units
Speed = kilometers/hour (distance/time)
Density = grams/mL (mass/volume)
Length
 SI
basic unit - meter (m)
distance btwn 2 objects
 use prefixes for larger/smaller
units
SI Prefixes – Page 74 - Common to Chemistry
Prefix
MegaKiloDeciCentiMilliMicroNanoPico-
Abbreviation Meaning Exponent
Million
M
106
thousand
k
103
tenth
d
10-1
hundredth
c
10-2
thousandth
m
10-3
millionth
10-6

billionth
n
10-9
trillionth
P
10-12
Volume
 Space
occupied by matter
 Calculated for solid…length x width x
height
 derived from units of length
unit = cubic meter
 Everyday unit = Liter (L), non-SI
 SI
 (Note: 1mL = 1cm3)
3
(m )
Devices for Measuring Liquid
Volume
 Graduated
cylinders
 Pipets
 Burets
 Volumetric
 Syringes
Flasks
Volume Changes!
 Volumes of a solid, liquid, or gas
generally increases w/ temp
 More prominent for GASES
 Therefore, measuring instruments
calibrated for specific temp
usually 20 oC, which is about room temp
Ex. Volumetric flask
Units of Mass
 Mass - quantity of matter present
Mass constant, regardless of location
Weight - force of “g”- changes w/
location
Working with Mass
 SI
unit - kilogram (kg)
everyday unit is gram (g)
measuring instrument: triple beam
balance
Units of Temperature
 Temp
- measures how hot/cold object
(Measured with a thermometer.)
is.
 Heat moves from hi - low temp
 2 temp scales:
◦ Celsius – named after Anders Celsius
◦ Kelvin – named after Lord Kelvin
Units of Temperature
 Celsius
scale
◦ Water Freezing point = 0 oC
◦ Water Boiling point = 100 oC
 Kelvin scale does not use degree sign,
just K
• absolute zero = 0 K
(no negative values)
• formula to convert: K = oC + 273
- Page 78
Units of Energy


Energy - ability to do work, or
produce heat
energy can be measured
 2 common units:
1) Joule (J) = SI unit of energy, named
after James Prescott Joule
2) calorie (cal) = heat needed to raise 1g
of water 1 oC
Units of Energy
Conversions
btwn joules &
calories carried out by using
following relationship:
1 cal = 4.184 J
Sec 3.3 Conversion factors
 A “ratio”
of equivalent measurements
 Start with two things that are the same:
one meter is one hundred centimeters
 write it as an equation
1 m = 100 cm
 Divide on each side of equation to come
up with 2 ways of writing the number “1”
Conversion factors
1m
100 cm
=
100 cm
100 cm
Conversion factors
1m
100 cm
=
1
Conversion factors
1m
100 cm
1m
1m
=
=
1
100 cm
1m
Conversion factors
1m
100 cm
1
=
=
1
100 cm
1m
Conversion factors
 unique
way of writing the # 1
 In same system they are defined
quantities so unlimited number of sig figs
big # small unit = small # big unit
100 cm = 1 m
Practice writing two possible
conversion factors for the
following:
 Between
kilograms and grams
 between feet and inches
 using 1.096 qt. = 1.00 L
What are they good for?
We can multiply by # “one” creatively to
change units
 Question: 13 inches is how many yards?
 We know that 36 inches = 1 yard
 1 yard
=1
36 inches
 13 inches x
1 yard
=
36 inches

What are they good for?
We can multiply by a conversion factor to
change the units .
 Problem: 13 inches is how many yards?
 Known: 36 inches = 1 yard.
 1 yard
=1
36 inches
 13 inches x
1 yard
=
0.36 yards
36 inches

Dimensional Analysis
 Method
of analyzing & solving problems,
by using units (dimensions) of
measurement
 Dimension = unit (g, L, cm)
 Analyze = solve
◦ Using units to solve problems
 If
units of answer correct, you probably
did math correctly!
Dimensional Analysis
 provides
alternative approach to problem
solving, instead of with equation or algebra.
 ruler is 12.0 inches long. How long is it in
cm? ( 1 inch = 2.54 cm)
 How long is this in meters?
 A race is 10.0 km long. How far is this in
miles, if:
◦ 1 mile = 1760 yards
◦ 1 meter = 1.094 yards
p. 82 practice problem #28
How many minutes are there in exactly one
week?
p. 83 practice problem # 30
An experiment requires that each student use an
8.5-cm length of magnesium ribbon. How many
students can do the experiment if there is a 570cm length of magnesium ribbon available?
Converting Between Units
 measurements
with one unit converted to
equivalent measurement with another unit
easily solved using dimensional analysis
 Sample: Express 750 dg in grams.
 Many complex problems are best solved
by breaking the problem into manageable
parts.
p. 84 practice problem #32
Using tables from this chapter, convert these:
a. 0.044 km to meters
b. 4.6 mg to grams
c. 0.107 g to centigrams
Converting Between Units
Let’s say you need to clean your car:
1) Start by vacuuming the interior
2) Next, wash the exterior
3) Dry the exterior
4) Finally, put on a coat of wax
• What problem-solving methods can help you
solve complex word problems?
 Break the solution down into steps, and use
more than one conversion factor if necessary

p. 85 practice problem # 34
(p. 30 in workbook)
The radius of a potassium atom is 0.227 nm.
Express this radius in the unit centimeters.
Converting Complex Units?
Complex units are those that are
expressed as a ratio of two units:
◦ Speed might be meters/hour
 Sample: Change 15 meters/hour to
units of centimeters/second
 How do we work with units that are
squared or cubed? (cm3 to m3, etc.)

BONUS: Crash of Flight 143 – see my webpage
- Page 86
Section 3.4 Density
 Which is heavier- a pound of steel or
a pound of styrofoam?
Most people answer “steel”, but the
weight is exactly the same
They are normally thinking about
equal volumes of the two
 The relationship here between mass
and volume is called Density
Density
 The
formula for density is:
mass
volume
Density =
• Common units are: g/mL, or
3
g/cm , (or g/L for gas)
• Density is a physical property, and
does not depend upon sample size
• A gold nugget has the same density as a
gold bar
- Page 90
Note temperature and density units
Density and Temperature

What happens to the density as the
temperature of an object increases?
Mass remains the same
Most substances increase in volume as
temperature increases
 Thus, density
generally decreases as
the temperature increases
Density and Water
 Water
is an important exception to
the previous statement.
 Over certain temperatures, the volume
of water increases as the temperature
decreases (You don’t want your water
pipes to freeze in the winter, right?)
Why does ice float in liquid water?
- Page 91
- Page 92