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!