Chapter 3
Scientific
Measurement
Measurements are essential !!
• One of your most important skills in
chemistry is making measurements
Measurement
 Has both a quantity and a unit
 Ex. 125.3mL
 125.3g
Types of Measurements
• Quantitative measurements- give
results in definite form, usually numbers
– Ex. A child’s temperature is 101.2oF
• Qualitative measurements – give
results in descriptive nonnumeric form
– Ex. A child feels feverish
Quantitative or Qualitative?
•
•
•
•
•
•
•
The plant is growing fast
John wears a size 8 shoe
The candle weighs 90g
The flame is hot
Wax is soft
The boy grew 12cm
Lead is very dense
When making measurements, you
can only estimate
1 digit !!!!!!!!!
Measuring Length
• Length – (meters) – use meter stick
or metric ruler.
– Calibrated in cm.
0cm
1cm
2cm
Measuring Mass
• Mass =the amount of matter in a
substance
• Measured in grams (g)
• Use digital balance up to 400 grams
• Triple beam balance used for heavier
masses
Digital Balance
• Make sure balance is set on grams
• Place empty container on balance.
• Hit “Tare” or “Zero” button to
remove the mass of the container.
• Add chemical to amount needed.
Triple Beam
Balance
• Make sure riders are set at zero.
• Start with middle rider. Move until
it’s too much, then move back one
notch.
• Then move back rider. Move until it’s
too much, then move back one notch.
• Slide front rider until it balances.
• Add amounts of riders together.
Liquid Volume
• Volume =the amount of space it
takes up.
• Measured in mL.
• Use graduated cylinders.
• Read bottom of meniscus, except in
liquids like mercury that curve
upward.
Solid Volume
• Regular shape – use formula (cm3)
–
–
–
–
Rectangle or cube = L x W x H
Cylinder = πr2 x H
Cone = 1/3 x πr2 x H
Sphere = 4/3 x πr3
• Irregular shape – water displacement
(mL)
– Collect water from overflow can or
measure how much level goes up
1mL = 1
3
cm
* Know this conversion factor !!!!!
Weight
• Weight =the pull of gravity on
an object.
• Measured in newtons.
• Use spring scale.
Density
Density
Density
 Ratio of mass to volume
 No set unit, depends of unit of mass and
volume
 g/cm3 or g/mL, etc.
Density = mass/volume
Ws. Density Problems ( with answers)
 Ws. Density Problems (II)
Indirect Measurement
 Used when matter is too large or too small to
measure
 Ex. To find the thickness of 1 playing
card, find thickness of 100 cards and
divided answer by 100.
How could you find the density of a
concrete patio?
What is the difference between
the terms precision and
accuracy?
Accuracy and Precision
 Accuracy- how close the
measurement is to accepted value
 Precision- how close a series of
measurements are to each other.
Three students made multiple weighings of a copper
cylinder, each using a different balance. Describe the
accuracy and precision of each student’s
measurements if the correct mass of the cylinder is
47.32g
Weighing 1
Lisa
47.03
Lamont
47.34
Leigh
47.95
Weighing 2
47.94
47.39
47.91
Weighing 3
46.83
47.31
47.90
Weighing 4
47.47
47.33
47.93
Accurate
& precise
Inaccurate
& precise
Inaccurate
& imprecise
“Calibrating” an instrument improves
it’s accuracy
Calculating Error
 Ex. Thermometer in pure boiling water reads
99.1oC (experimental value)
 Accepted value is 100oC
 Error = experimental value - accepted
value
99.1oC - 100oC = -0.9oC
* Can be a positive or negative number
Percentage Error
error
Percentage =
error
accepted value
= 0.9oC
X 100
100.0oC
= 0.9%
X 100
Ws. Percent Error Problems
Scientific Notation
 Used to show large or small numbers
 602,000,000,000,000,000,000,000 is
written 6.02 x 1023
Coefficient
Shows power of 10
Greater or equal to 1, and
less than 10
( number of places decimal was moved)
 If you move the decimal to the left, power is a




positive number
If you move the decimal to the right, the power is a
negative number.
Ex.
0.000 000 000 000 000 000 000 327g
Is written: 3.27 x 10-22
Practice Problems
 84,000 =
 6,300,000 =
 0.00025 =
 0.000 008 =
 0.00736 =
Multiplication with Scientific
Notation
 Multiply the coefficients and Add the
exponents.
(3 x 104) x ( 2 x 102)= 6 x 106
(2.1 x 103) x (4.0 x 10-7) = 8.4 x 10-4
Division with scientific notation
Divide the coefficients and Subtract the
exponent in denominator by exponent in
numerator
3.0 x 105
=
2
6.0 x 10
0.5 x 103
= 5.0 x 102
Addition and Subtraction with
Scientific notation
 When adding or subtracting the exponents
must be the same
 Ex.
5.4 x 103 and 8.0 x 102
Change: 8.0 x 102 = 0.80 x 103
Then add (or subtract) coefficients:
5.4 x 103 + 0.80 x 103 = 6.2 x 103
Ws. Scientific Notation
Significant Figures
 All measurements must be
reported with the correct
number of significant figures
in order to calculate the
answer.
What is a Significant Figure?
 “Sig-Figs” include all the digits known plus
the last digit that is estimated
 Ex.
 You use the scale in the produce section of
the store to get an approximate weight of
your vegetables. The scale is calibrated in
0.1lb intervals Your vegetables are between
2.4 and 2.5lbs.so you estimate its weight to
be 2.46lbs.
 Your answer has three significant figures
Significant figures
 All non-zero numbers are always significant
 Zeros are tricky…..
 Leading zeros- NEVER significant (0.005)
 Captive zeros- ALWAYS significant (505)
 Trailing zeros- SOMETIMES….
(decimal-yes otherwise no)
5.000 (yes) 5,000 (no)
“Sig-Fig” Rules
1. All nonzero digits are assumed
significant.
Ex.
24.7meters,
7.43meter and
714meters
-all have three significant figures
2.
Zeros appearing between nonzero digits are
significant.
Ex.
7003 meters
40.79 meters
1.503 meters
-all have four significant figures
3.
Leftmost zeros appearing in front of nonzero
digits are NOT significant. (They are
placeholders)
Ex.
0.0071 meters
0.42 meters
0.000 099 meters
-all have only two “sig-figs”.
-You can eliminate the zeros by writing it in
scientific notation
7.1 x 10-3 meter
4.2 x 10-1 meter
9.9 x 10-5 meter
4. Zeros at the end of a number and to the
right of a decimal point are always
significant.
Ex.
43.00 meters
1.010 meters
9.000 meters
-all have four significant figures
5. Trailing Zeros at the rightmost end
of a measurement are NOT
significant (They are placeholders)
Ex
300m – has 1 “sig-fig”
7000m – has 1 “sig-fig”
27,210m – has 4 “sig-figs”
6. There are two situations when you
have an unlimited number of “sigfigs”.
1. Counting – Ex. 23 people in the
classroom
2. Using exactly defined
quantities.
Ex. 60min. = 1 hour
500 pages = 1 ream
How many “Sig-figs” are there?
 123m =
(3)
 40,506mm =
(5)
 9.8000 x 104 m =
 22 meter sticks =
 0.07080 m =
 98,000 m =
(5)
(unlimited)
(4)
(2)
Why are Sig-Figs So Important?
© Copyrght, 2001, L. Ladon. Permission is granted to use and duplicate these materials for
non-profit educational use, under the following conditions: No changes or modifications will
be made without written permission from the author.
 Being careless with significant figures may result in dire
consequences. The following is a true story told to me by a Baltimore
County middle school teacher concerning their mishap resulting
from not considering the significance of significant figures:
 The science teachers at a Baltimore County middle school wished to
acquire a steel cube, one cubic centimeter in size to use as a visual aid
to teach the metric system. The machine shop they contacted sent
them a work order with instructions to draw the cube and specify its
dimensions. On the work order, the science supervisor drew a cube
and specified each side to be 1.000 cm. When the machine shop
received this job request, they contacted the supervisor to double
check that each side was to be one centimeter to four significant
figures. The science supervisor, not thinking about the "logistics",
verified four significant figures.
 When the finished cube arrived approximately one month
later, it appeared to be a work of art. The sides were mirror
smooth and the edges razor sharp. When they looked at the
"bottom line", they were shocked to see the cost of the cube
to be $500! Thinking an error was made in billing, they
contacted the machine shop to ask if the bill was really $5.00,
and not $500. At this time, the machine shop verified that the
cube was to be made to four significant figure specifications.
It was explained to the school, that in order to make a cube
of such a high degree of certainty, in addition to using an
expensive alloy with a low coefficient of expansion, many
man hours were needed to make the cube. The cube had to be
ground down, and measured with calipers to within a certain
tolerance. This process was repeated until three sides of the
cube were successfully completed. So, "parts and labor" to
prepare the cube cost $500. The science budget for the school
was wiped out for the entire year. This school now has a steel
cube worth its weight in gold, because it is a very certain
cubic centimeter in size.
Significant figures
 All non-zero numbers are always significant
 Zeros are tricky…..
 Leading zeros- NEVER significant (0.005)
 Captive zeros- ALWAYS significant (505)
 Trailing zeros- SOMETIMES….
(decimal-yes otherwise no)
5.000 (yes) 5,000 (no)
Use “Oceans” to determine Sig-Figs
Pacific
Decimal “Present”
Atlantic
Decimal “Absent”
Start counting with first nonzero number
and count all numbers after it.
Using “Sig-Figs” when
Calculating
 A calculated answer can not be more precise than
the least precise measurement used in the
calculation
For multiplication and division use least
# of sig-figs in measurements you are
multiplying or dividing
Try this:
6.9cm x 0.0876cm
 Multiply or divide numbers
 Put into scientific notation
 Round to the correct # of sig-figs
7.7 meters
5.4 meters
7.7m x
5.4m
=
41.58 sq. meters
Since measurements
Answer can only
then
only have 2 “sig-figs”
have 2 “sig-figs”
Round answer to appropriate number of “sig-figs”
= 4.2 x 101 square meters
For addition and subtraction use least
number of decimal places in
measurements you are adding or
subtracting
2.45g + 4.987g = 7.437g
= 7.44g
Take the following answers and round
each to the correct number of significant
figures. Be sure to include the unit label.
(14.3g )÷ (2.03cm3) = 7.0443348g/cm3
7.04g/cm3
3.004m x 26.4m = 79.3056m2
7.93 x 101m2
301.00 L – 99.8643 L = 201.1357L
2.01 x 102L
Math Rules for Sig Fig
Multiplying and dividing sig fig
Your answer can only have as many sig
fig as the least sig fig in the problem
Math Rules for Sig Fig
Adding and subtracting
Your answer can only have as many
decimal places as the least in the
problem
Rounding Problems
 Round each measurement to the number of “sig-figs”
shown in parentheses. Write answers in scientific
notation first !!!!
 314.721 meters (four)
 0.001 775 meters (two)
 8792 meters (two)
= 3.147 x 102
= 1.8 x10-3
= 8.8 x 103
Meters, Liters and Grams - YouTube
The International System
of Measurement (SI)
• Metric System was developed in
France in 1795
• Revised and called International
System of Measurements (SI) in
1960
• Based on units of ten
SI Base Units
Quantity
symbol
Length
SI base
unit
Meter
Mass
gram
g
Temperature
Time
Kelvin
Celsius
Second
K
oC
s
Liquid volume
Liter
L
Amount of
substance
Mole
mol
m
Metric Prefixes and
Abbreviations
“Kids haven’t died by doing crazy metric”
kilo
hecto deka basic deci centi milli
(k)
(h)
unit
(da) (m,L,g)
(d)
(c )
(m)
Memorize these !!!!!
* “unit” means meter, liter or grams
 1 Kilo = 1000 units
 1 Hecto = 100 units
 1 Deka = 10 units
 Basic unit = 1
 10 deci = 1 unit
 100 centi = 1 unit
 1000 milli = 1 unit
1Giga(G) = 1 x 109 units
1Mega(M) = 1 x 106units
1 x 106 Micro(µ) = 1 unit
1 x 109 Nano(n) = 1 unit
1 x 1012 Pico(p) = 1 unit
Conversion factors
 A ratio of equivalent measurements
 Ex.
1 dollar = 4 quarters = 10
dimes = 100 pennies
1 dollar
4 quarters
or
4 quarters
1 dollar
Other Conversion factors
 1 week = 7 days
 1 year = 365 days
 1 decade = 10 years
 1 century = 100 years
 24 hours = 1 day
 1 hour = 60 min.
 60 sec = 1 min
 1 ft. = 12 in.
 1 yd = 36 in
 1 yd = 3 ft.
 5280 ft = 1 mile
Dimensional Analysis
 A way to solve problems using units,
dimensions or measurements
 Use “T” boxes
 Start with known, work toward unit
you want
 Ex. How many seconds in 8 hours?
Practice problems
(use “T” boxes)
 3500 days = ______________ years
 4000 days = _______________ decades
 83,972.7 minutes = ____________weeks
 546 months = _______________ century
 5.6 km = _________________ mm
Converting Metric Units to Metric
units (2 step-process)
 Go from “known” to a basic unit, then basic unit
to unit you want.
236.6 kg = __________cg
Try this one…….
 2,998,766 cL = ________________hL
3.9 x 1014 decigrams = ____
Gigagrams?
 Use “T” boxes-
 convert into basic unit, then to unit needed
3.9 x1014 dg
g
dg
=
3.9 x 106Gg
Gg
g
If two “knowns” or “per”……. Use
Double “T” box and Fix one at a
time.
 If a car is traveling at 65
kilometers per hour, what is its
speed in meters per second?
Writing answers correctly
 Must be in scientific notation
 Must have correct number of significant
figures.
 Don’t count the sig-figs in conversion factors
 Count sig-figs in “known” and put the answer in
the same number of sig-figs.
Heat (Thermal Energy)
• The energy in the motion of
atoms and molecules
The more heat energy in matter, the
faster the atoms or molecules move.
Temperature
- the average kinetic( motion) energy of
molecules in a substance.
- measured using a thermometer.
Measuring heat energy
calorie - the amount of heat needed to
raise 1 gram of water 1oC.
1 calorie = 4.18 joules (SI unit of energy)
Btu ( British thermal unit) = 252 calories
or the amt. of thermal energy to raise 1
pound of water 1oF
Specific Heat
-different substances absorb different
amounts and therefore get “hotter” at
different rates.
- Specific heat is the amount of heat needed
to raise 1 gram of a substance 1 degree
celsius
Specific Heat=calories
gramoC
-abbreviated “c”
Calculating Heat Change
Change in
temperature
Heat in calories
Q= mcDT
Mass in grams
Specific heat
Specific Heat Chart
Substance
Specific heat
Water
Aluminum
Iron
Copper
Zinc
Silver
Lead
1.0
0.215
0.11
0.092
0.091
0.052
0.04
The Law of Dulong and Petit
Dulong
Petit
-they found that s.h. depends
on # of atoms/gram.
Heavier atoms = fewer atoms/g = lower s.h.
1 gram
Heat up faster
(lower s.h.)
1 gram
Heat up slower
(higher s.h.)
-the less atoms/gram means more
energy for each atom and therefore
they heat up faster.
Specific Heat Chart
Substance
(atomic Mass)
Water (18.0)
Aluminum
(26.98)
Iron (55.85)
Copper (63.55)
Zinc (65.39)
Silver (107.87)
Lead (207.2)
Specific heat
1.0
0.215
0.11
0.092
0.091
0.052
0.04
The higher the specific
heat, the more heat it
needs to raise its
temperature.
Ws. Specific Heat Problems
Temperature Scales
Fahrenheit Celsius Kelvin
Water
Boils
Water
Freezes
Molecular
Motion
Stops
212oF
100oC
373K
32oF
0o C
273K
-460oF
-273oC
0K
(absolute
zero)
Converting between
Temperature Scales
From Fahrenheit to Celsius:
oC
= 5/9 (oF-32)
Ex. What is the Celsius value for 60.0oF?
oC = 5/9(60-32)
oC = 5/9(28)
oC = 15.55
oC
=15.6 ( look at Sig-Figs of
other temperature reading)
From Celsius to Fahrenheit:
oF
=(9/5 x
oC)
+ 32
Ex. What is the Fahrenheit value for
85.0oC?
oF
= (9/5 x
oF
= (153) + 32
oF
= 185
85.0)
+ 32
From Celsius to Kelvin:
K =
oC
+ 273
Ex. 80.0oC would be what value on the
Kelvin scale?
K
= 80 +
K = 353
273
From Kelvin to Celsius:
oC
= K - 273
Ex. 459K would be what value on
the Celsius scale?
oC
=
459 - 273
oC
= 186
From Fahrenheit to Kelvin:
K = 5/9 (oF + 460)
Ex. What would 45.0oF be on the
Kelvin scale?
K = 5/9(45 + 460)
K = 5/9(505)
K = 280.55 = 281
From Kelvin to Fahrenheit:
oF
= (9/5 x K ) - 460
Ex. 690.K would be what value on
the Fahrenheit scale?
oF
= (9/5 x 690) - 460
oF
= (1242) - 460
oF
= 782
Liquid Thermometers
-Work on the principle of thermal
expansion.
- the expansion of the liquid is
proportional to the change in
temperature.
-silver- mercury
- red- alcohol
Digital thermometers
-measure change in electrical
resistance in a wire caused by
temperature change.
Liquid Crystal
Thermometers
- crystals between thin sheets of
plastic change as temperature
increases, causing them to change
structure and color.
Ws. Temperature Conversions
Ws. Temperature Conversions
( word Problems)
Review for Test
 Know how to put # into scientific notation
 Know how to determine Sig-Figs and how many should be
in the answer.
 Measurements must be in scientific notation, correct
sig-figs and have a unit.
 Be able to convert from unit to another. Mulitply across top
then= and divide across the bottom
 Conversion factors – above and below must be equal.
Cross out unit if on top and bottom.
 Metric Conversion- unit you have to basic unit to unit
you want
Review for Test
 Know the terms accuracy and precision
 Know that the density of water is 1g/mL
 Know that 1 mL = 1 cm3
 Define temperature
 Calculate specific heat problems
 Dulong and Petit
 Know how water displacement is used to find
volume
 Know how to manipulate the density equation
Memorize these !!!!!
* “unit” means meter, liter or grams
 1 Kilo = 1000 units
 1 Hecto = 100 units
 1 Deka = 10 units
 Basic unit = 1
 10 deci = 1 unit
 100 centi = 1 unit
 1000 milli = 1 unit
1Giga(G) = 1 x 109 units
1Mega(M) = 1 x 106units
1 x 106 Micro(µ) = 1 unit
1 x 109 Nano(n) = 1 unit
1 x 1012 Pico(p) = 1 unit
Formulas You MUST Know
 % error = error/ accepted value x 100
 Density = mass/volume
 Specific heat Q=mc∆T
 Celsius to Kelvin- add 273 to Celsius temperature
Ws. Problem Solving
Last Hint
 Look over all practice worksheets, especially Dimensional
analysis problems and metric conversions!!!!!