Transcript Measurement
3.1 Measurements and Their
Uncertainty
Measurement
Quantity that has both a
number and unit
Example: Height = 67 inches
The units typically used in
science are those of the
International System of
Measurements (SI)
More to come…
3.1 Measurements and Their
Uncertainty
Scientific Notation
A given number is written as the product of two
numbers
A coefficient
10 raised to a power
602,000,000,000,000,000,000,000 = 6.02 x 1023
3.1 Measurements and Their
Uncertainty
Accuracy
A measure of how close a
measurement comes to the actual
or true value of whatever is
measured
Closest to the bull’s eye
Precision
A measure of how close a series
of measurements are to one
another
All darts in same area but not
near bull’s eye
3.1 Measurements and Their
Uncertainty
Accepted Value
The correct value based on reliable references
Experimental Value
The value measured in the lab
Error
The difference between the experimental value and the
accepted value
Error = Experimental Value – Accepted Value
Error can be positive or negative
Example: The boiling point of water is 100.0°C and was
measured in the lab at 99.1°C
What is the Error?
3.1 Measurements and Their
Uncertainty
Percent Error
Also known as relative error
The absolute value of the error divided by the accepted
value
Percent Error = ___/error/___ x 100%
accepted value
Because of the absolute value, Percent Error will always
be positive
Example: The boiling point of water is 100.0°C and
was measured in the lab at 99.1°C
What is the Percent Error?
3.1 Measurements and Their
Uncertainty
Significant Figures
Rule 1:
Every nonzero digit is significant
Example: 24.7 has 3 significant figures
2.47 x 101 has 3 digits in the coefficient
Rule 2:
Zeroes between nonzero digits are significant
Example: 7003 has 4 significant figures
7.003 x 103 has 4 digits in the coefficient
3.1 Measurements and Their
Uncertainty
Significant Figures
Rule 3:
Leftmost zeroes in front on nonzero digits are not
significant; they act as placeholders
Example: 0.0071 has 2 significant figures
7.1 x 10-3 has 2 digits in the coefficient
Rule 4:
Zeroes at the end of a number and to the right of a
decimal point are significant
Example: 43.00 has 4 significant figures
Think about measuring and sensitivity
3.1 Measurements and Their
Uncertainty
Significant Figures
Rule 5:
Zeroes at the rightmost end that lie to the left of an understood
decimal point are not significant
Example: 300 has 1 significant figure
Should be written as 3 x 102 to show this
Rule 6:
There are 2 situations in which numbers have an unlimited
number of significant figures
When counting
Example: There are 28 students in this classroom
When writing conversions
Example: 60 min = 1 hr
3.1 Measurements and Their
Uncertainty
Significant Figures in
Measurements
All of the digits that are
known, plus a last digit
that is estimated
Figure 3.5 (p. 67)
Tenths place,
hundredths place,
thousandths place
3.1 Measurements and Their
Uncertainty
Significant Figures in Calculations
A calculated answer cannot be more precise than the
least precise measurement from which it was calculated
Rounding
Decide on the number of significant figures and round to
that many digits, rounding to the left
If digit to the right is less than 5, drop it!
If digit is 5 or more, value of last digit is increased by 1
314.721 meters (four)
0.001755 meter (two)
8792 meters (two)
3.1 Measurements and Their
Uncertainty
Addition and Subtraction
Round to the same number of decimal places as the
measurement with the least number of decimal places
12.52 m + 349.0 m + 8.24 m = 369.76 m
Rounded to correct number of sig figs = ?
Multiplication and Division
Round to the same number of significant figures as the
measurement with the least number of significant
figures
7.55 m X 0.34 m = 2.567 m2
Rounded to correct number of sig figs = ?
3.1 Measurements and Their
Uncertainty
Now is your chance to practice!
Work on it individually.
Let’s grade it now!
3.2 The International System of Units
The International System of Units
Abbreviated SI
Metric system in multiples of 10
7 base units
Quantity
Length
Mass
Temperature
Time
Amount of substance
Luminous intensity
Electric current
SI Base Unit
Symbol
3.2 The International System of Units
The International System of Units
Abbreviated SI
Metric system in multiples of 10
7 base units
Quantity
Use mainly
Length
the first 5
SI Base Unit
Symbol
meter
m
Mass
kilogram
kg
Temperature
kelvin
K
Time
second
s
Amount of substance
mole
mol
Luminous intensity
candela
cd
Electric current
ampere
A
3.2 The International System of Units
Units of Length
Standard is the meter, abbreviated m
If small, may use the centimeter (cm)
or the millimeter (mm)
100cm = 1m
1000mm = 1m
If large, may use the kilometer (km)
1000m = 1km
3.2 The International System of Units
Units of Mass
Remember the standard of mass – the kilogram!
Abbreviate kg
Can also use the gram (g), milligram (mg), or
microgram (μg)
1000g = 1kg
1000mg = 1g
1000000μg = 1g
3.2 The International System of Units
Units of Temperature
Celsius scale
Freezing point of water = 0°C
Boiling point of water = 100°C
Kelvin scale
Freezing point of water = 273K
Boiling point of water = 373K
Conversion
K = °C + 273
What is the Kelvin temperature for 35°C?
What is the Celsius temperature for 313K?
Vide
o
3.2 The International System of Units
Units of Time
Measured in seconds (s), minutes (min),
and hours (hr)
No different from what we use!
Conversion
60s = 1min
60min = 1hr
3.2 The International System of Units
Amount of a Substance
The mole
Will be discussed later…
What about others?
What do you think we may be missing?
3.2 The International System of Units
Units of Volume
Two main types:
If a liquid, usually measured in the
liter (L)
May also use milliliter (mL) for small
amounts
1000mL = 1L
If a solid, can multiply
length x width x height (in cm)
This will give us the volume in cubic
centimeters (cm3)
3.2 The International System of Units
Units of Energy
The joule (J)
Named after English physicist James Prescott Joule
The calorie (cal)
Quantity of heat that raises the temperature of 1g of pure
water by 1°C
Look at packaging for European products
Conversion
1J = 0.2390 cal
1cal = 4.184J
3.2 The International System of Units
Metric prefixes
Prefix
Meaning
Factor
mega (M)
1 million times larger
106
kilo (k)
1000 times larger
103
deci (d)
10 times smaller
10-1
centi (c)
100 times smaller
10-2
milli (m)
1000 times smaller
10-3
micro (μ)
1 million times smaller
10-6
nano (n)
1000 million times smaller
10-9
pico (p)
1 trillion times smaller
10-12
3.3 Conversion Problems
Conversion Factor
A ratio of equivalent measurements
1m = 100cm = 1
1m
1m
The numerator (top) is equal to the denominator
(bottom)
Like making change! 4 quarters is one dollar.
3.3 Conversion Problems
Dimensional Analysis
A way to analyze and solve problems using the units, or
dimensions, of the measurements
Example: How many seconds are in a workday?
8h x 60 min x 60 s = 28,800 s
1h
1 min
Now you try!
How many minutes are in one week?
How many seconds are in a 40-hour
work week?
3.3 Conversion Problems
Converting Between Units
Example: Express 750dg in grams
750dg x 1g = 75g
10dg
Now you try!
Express 0.044km in meters
Express 0.073cm in micrometers
3.3 Conversion Problems
Converting Complex Units
Many common measurements are in a ratio of two units
Speed in miles per hour (m/h)
Light speed is 3.00 x 1010 cm/s. What is the speed of
light in kilometers per hour?
3.00 x 1010 cm x 1m
x 1km x 60s x 60min = ?
1s
100cm 1000m 1min 1h
3.4 Density
Which is heavier: a pound of lead or a pound of
feathers?
3.4 Density
They are the same!
Why do we think the lead is instinctively?
Density
Density is an intensive property (depends on the type of
matter)
3.4 Density
What about a helium balloon?
It floats because it is less dense than air.
What about hot air balloons?
Density greatly decreases as temperature
increases
3.4 Density
Density = m
v
Units are in the form of g/cm3
Lets practice
A copper penny has a mass of 3.1g and a volume of
0.35 cm3. What is the density of copper?
Density = mass__ = 3.1 g__ = 8.9g/cm3
volume 0.35 cm3
This is rounded to 2 sig figs
3.4 Density
Lets try and solve for mass using the density
What is the volume of a pure silver coin that has a mass
of 14 g and density of 10.5 g/cm3?
Now, lets see it in action in the lab!