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Ch. 5 Notes---Scientific Measurement
Qualitative vs. Quantitative
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Qualitative measurements give results in a descriptive nonnumeric
adjective describing
form. (The result of a measurement is an _____________
the object.)
short
heavy
cold
*Examples: ___________,
___________,
long, __________...
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Quantitative measurements give results in numeric form. (The
number
results of a measurement contain a _____________.)
600 lbs.
5 ºC
*Examples: 4’6”, __________,
22 meters, __________...
Accuracy vs. Precision
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single
Accuracy is how close a ___________
measurement is to the
true __________
value
________
of whatever is being measured.
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several measurements are to
Precision is how close ___________
each ___________.
other
_________
Practice Problem: Describe the shots for the targets.
Bad Accuracy & Bad Precision
Good Accuracy & Bad Precision
Bad Accuracy & Good Precision
Good Accuracy & Good Precision
Significant Figures
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Significant figures are used to determine the ______________
precision
of a
measurement. (It is a way of indicating how __________
precise a
measurement is.)
*Example: A scale may read a person’s weight as 135 lbs. Another
scale may read the person’s weight as 135.13 lbs. The ___________
second
more significant figures in the
scale is more precise. It also has ______
measurement.
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Whenever you are measuring a value, (such as the length of an object
with a ruler), it must be recorded with the correct number of sig.
figs.
ALL the numbers of the measurement known for sure.
Record ______
Record one last digit for the measurement that is estimated. (This
reading in between the
means that you will be ________________________________
marks of the device and taking a __________
guess
__________
at what the next
number is.)
Significant Figures
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Practice Problems: What is the length recorded to the correct
number of significant figures?
length = ________cm
11.65
(cm) 10
20
30
40
length = ________cm
58
50
60
70
80
90
100
Rules for Counting Significant Figures in a Measurement
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When you are given a measurement, you will need to be aware of how
many sig. figs. the value contains. (You’ll see why later on in this
chapter.)
Here is how you count the number of sig. figs. in a given measurement:
#1 (Non-Zero Rule): All digits 1-9 are significant.
3
*Examples: 2.35 g =_____S.F.
2 S.F.
2200 g = _____
#2 (Straddle Rule): Zeros between two sig. figs. are significant.
3
4
*Examples: 205 m =_____S.F.
80.04 m =_____S.F.
5
7070700 cm =_____S.F.
#3 (Righty-Righty Rule): Zeros to the right of a decimal point AND
anywhere to the right of a sig. fig. are significant.
3
3
*Examples: 2.30 sec. =_____S.F.
20.0 sec. =_____S.F.
4
0.003060 km =_____S.F.
Rules for Counting Significant Figures in a Measurement
#4 (Bar Rule): Any zeros that have a bar placed over them are sig.
(This will only be used for zeros that are not already significant
because of Rules 2 & 3.)
4
*Examples: 3,000,000 m/s =_____S.F.
2
20 lbs =____S.F.
#5 (Counting Rule): Any time the measurement is determined by
simply counting the number of objects, the value has an infinite
number of sig. figs. (This also includes any conversion factor
involving counting.)
∞
∞
*Examples: 15 students =_____S.F.
29 pencils = ____S.F.
7 days/week =____S.F.
∞
60 sec/min =____S.F.
∞
Calculations Using Sig. Figs.
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When adding or subtracting measurements, all answers are to be
rounded off to the least # of ___________
found in
decimal __________
places
the original measurements.
Example:
+
≈ 157.17
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(only keep 2 decimal places)
When multiplying or dividing measurements, all answers are to be
significant_________
figures found in the
rounded off to the least # of _________
original measurements.
Practice Problems:
(only keep 1
decimal place)
4.7 cm
2.83 cm + 4.009 cm − 2.1 cm = 4.739 cm ≈_____
98 m2
36.4 m x 2.7 m = 98.28 m2 ≈ _____
(only keep 2 sig. figs)
5.9 g/mL
0.52 g ÷ 0.00888 mL = 5.855855 g/mL ≈ ____
(only keep 2
sig. figs)
So What Does This All Mean?
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When you measure and you then use a calculator you need to think
about how many decimal places in your answer.
When you use your calculator and multiply or divide give me three
to five significant figures (or numbers).
Don’t give me tons of decimal places.
Practice Problems:
4.7 cm
2.83 cm + 4.009 cm − 2.1 cm = 4.739 cm ≈_____
98 m2
36.4 m x 2.7 m = 98.28 m2 ≈ _____
(least amount of
decimal places)
(least amount of sig figs)
amount of
0.52 g ÷ 0.00888 mL = 5.855855 g/mL ≈ 5.9
____ g/mL(least
sig figs)
For Example
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Lets say you are finding the average mass of beans. You would
count how many beans you had and then find the mass of the
beans.
26 beans have a mass of 44.56 grams.
44.56 grams ÷26 =1.713846154 grams
So then what should your written answer be?
How many decimal points did you have in
your measurement?
2
Rounded answer = 1.71 grams
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The SI System (The Metric System)
Here is a list of common units of measure used in science:
Standard Metric Unit
Quantity Measured
mass
kilogram, (gram)
______________
length
meter
______________
volume
cubic meter, (liter)
______________
seconds
______________
time
temperature
Kelvin, (˚Celsius)
_____________
The following are common approximations used to convert from our
English system of units to the metric system:
1 yard
1 m ≈ _________
2.2 lbs.
1 kg ≈ _______
1.609 km ≈ 1 mile
mass of a small paper clip
1 gram ≈ ______________________
sugar cube’s volume
1mL ≈ _____________
1 L ≈ 1.06 quarts
dime
1mm ≈ thickness of a _______
The SI System (The Metric System)
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Metric Conversions
The metric system prefixes are based on factors of _______.
Here is a
mass
list of the common prefixes used in chemistry:
kilo- hecto- deka-
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deci- centi- milli-
The box in the middle represents the standard unit of measure such as
grams, liters, or meters.
Moving from one prefix to another involves a factor of 10.
cm = 10 _____
dm = 1 _____
m
*Example: 1000 millimeters = 100 ____
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The prefixes are abbreviated as follows:
k
h
da
g,
L,
m
d
grams
c
Liters
m
meters
*Examples of measurements: 5 km 2 dL 27 dag 3 m 45 mm
Metric Conversions
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To convert from one prefix to another, simply count how many places you move on
the scale above, and that is the same # of places the decimal point will move in the
same direction.
Practice Problems:
380,000
380 km = ______________m
0.00145
1.45 mm = ______________m
4.61
461 mL = ____________dL
0.0004 dag
0.4 cg = ______________
260 mg
0.26 g =_____________
230
230,000 m = _______km
Other Metric Equivalents
1 mL = 1 cm3
1 L = 1 dm3
For water only:
1 L = 1 dm3 = 1 kg of water
or
1 mL = 1 cm3 = 1 g of water
Practice Problems:
0.3 L
(1) How many liters of water are there in 300 cm3 ? ___________
50 kg
(2) How many kg of water are there in 500 dL? _____________
Metric Volume: Cubic Meter (m3)
10 cm x 10 cm x 10 cm = Liter
Area and Volume Conversions
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If you see an exponent in the unit, that means when converting
you will move the decimal point that many times more on the
metric conversion scale.
*Examples:
twice
cm2 to m2 ......move ___________
as many places
3 times as many places
m3 to km3 ......move _____
2
380,000,000
Practice Problems: 380 km2 = _________________m
3
0.00461
4.61 mm3 = _______________cm
k h
da g, L, m d c m
grams
Liters
meters
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Scientific Notation
Scientific notation is a way of representing really large or small
numbers using powers of 10.
*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles
0.000 000 042 mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
(1) Write down all the sig. figs.
(2) Put the decimal point between the first and second digit.
(3) Write “x 10”
(4) Count how many places the decimal point has moved from its
original location. This will be the exponent...either + or −.
(5) If the original # was greater than 1, the exponent is (__),
+ and if the
−
original # was less than 1, the exponent is (__)....(In
other words, large
+ exponents, and small numbers have (_)
− exponents.
numbers have (__)
Scientific Notation
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Practice Problems: Write the following measurements in scientific
notation or back to their expanded form.
477,000,000 miles = _______________miles
4.77 x 108
0.000 910 m = _________________
9.10 x 10−4 m
−
9
6,300,000,000
6.30 x 10 miles = ___________________ miles
0.00000388 kg
3.88 x 10−6 kg = __________________
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Mass vs. Weight
Mass depends on the amount of
___________
in the object.
matter
Weight depends on the force of
____________
acting on the object.
gravity
Weight
______________
may change as you
move from one location to another;
mass
____________
will not.
Mass = 80 kg
mass
You have the same ____________
on
the moon as on the earth, but you
weigh
___________
less since there is less
gravity on the moon.
_________
Weight = 176 lbs.
Mass = 80 kg
Weight = 29 lbs.
Density
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Density is a ___________
ratio
of an object’s mass and its volume.
size
Density does not depend on the _________
of the sample you have.
The density of an object will determine if it will float or sink in
less dense than the other
another phase. If an object floats, it is _______
more
substance. If it sinks, it is ________
dense.
The density of water is 1.0 g/mL, and air has a density of
0.00129 g/mL (or 1.29 g/L).
Density = Mass/Volume
Mass = D x V
Density = m/V
Volume = m/D
m
D X
V
Density
Practice Problems:
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The density of gold is 19.3 g/cm3. How much would the mass of a
bar of gold be? Assume a bar of gold has the following dimensions:
L= 27 cm W= 9.0 cm H= 5.5 cm
Volume = L x W x H
Volume = 27 x 9.0 x 5.5 = 1336.5 cm3
mass = D x V
mass = 19.3 g/cm3 x 1336.5 cm3 = 25,794.45 g
mass ≈ 26,000 g = 26 kg ≈ 57 lbs.
(2) Which picture shows the block’s position when placed in salt water?
(3) Will the following object float
in water? _______
No! It will sink. (D > 1)
Object’s mass = 27 g
Object’s volume= 25 mL
Measuring Temperature
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Temperature is the ____________
hotness
or ____________
coldness
of an object.
The Celsius temperature scale is based on the freezing point and
water
boiling point of __________.
F.P.= 0˚C B.P.= 100˚C
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The Kelvin temperature scale, (sometimes called the “absolute temp.
lowest
scale” is based on the ____________
temperature possible, absolute
stop
zero. (All molecular motion would __________.)
Absolute Zero = 0˚ Kelvin = −273˚ C
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To convert from one temp. scale to another:
˚C = Kelvin − 273
K= Celsius + 273
Practice Problems: Convert the following
298 K
25˚C = _______
200
473 K = _______˚C
Temperature Scales
Liquid Nitrogen
Evaluating the Accuracy of a Measurement
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The “Percent Error ” of a measurement is a way of representing the
accuracy of the value. (Remember what accuracy tells us?)
% Error = (Accepted Value) − (Experimentally Measured Value) x 100
(Accepted Value)
(Absolute Value)
Practice Problem:
A student measures the density of a block of aluminum to be
approximately 2.96 g/mL. The value found in our textbook tells us
that the density was supposed to be 2.70 g/mL. What is the accuracy
of the student’s measurement?
% Error = |2.70−2.96| ÷ 2.70 0.096296…x 100 = 9.63% error
=