Transcript Measurements

Measurements
Measurements make
observations meaningful
International System of Units
(SI Units)
• Uses the metric system
– Based on units of 10
SI Units
Quantity
SI Unit
Symbol
Length
Meter
m
Mass
Gram
g
Time
Second
s
Temperature
Kelvin
K
Volume
Cubic meter
m3
Amount
mole
mol
Mass
• Mass and
weight are
NOT the
same thing
• Weight is
dependant
upon gravity,
mass is not
Temperature
•
Kelvin is the SI unit, but
Celsius (C) is often used
• K = C + 273
Practice:
1. Convert 25oC to K.
2. Convert 352K to oC.
3. Convert -15oC to K.
•
Heat and temperature are
not the same thing
–
–
Heat is a type of energy
Temperature is a
measurement of energy
Important Temperatures
• Freezing Points for water
0oC = 273K = 32oF
• Boiling Points for water
100oC = 373K = 212oF
• Absolute zero
0 K (-273oC)
Theoretically, all movement stops at this
temperature
Volume
• Cubic meter (m3) is the SI unit, but
liter (or milliliter) is often used
• Useful Information:
– Cubic centimeter (cm3 or cc) =
milliliter (mL)
– 1cc = 1mL
Moles
• Used to measure the amount (quantity)
of something
– 1 mole = 6.02 x 1023 particles
Density
•
•
•
How much “stuff” in a given area
Density of water (at 250C) = 1.00g/mL
D = m/v
Density Practice
1. A rock has a mass of 3.5kg and a volume
of 7.0m3. What is the rock’s density?
2. An object’s density is 8.0g/cm3 and its
mass is 1.5g. What is the object’s
volume?
3. What would the mass be of a 25mL
sample of an object with a density of
0.047g/mL?
Base Units of the Metric System
Quantity
Name
Symbol
Length
Meter
m
Mass
Gram
g
Volume
Liter
L
Energy
Joule
J
* Reference Table D
SI Prefixes
Prefix
Symbol
Meaning
Kilo-
k
1000
Hecto-
h
100
Deka-
da
10
Deci-
d
0.1 (1/10)
Centi-
c
0.01 (1/100)
Milli-
m
0.001 (1/1000)
* Reference Table C
Metric System
Conversions
• Kangaroos Hop Down
Large Green Mountains
During Christmas Morning
– As you move left, move the decimal to the left
– As you move right, move the decimal to the
right
Convert each measurement
1.
2.
3.
4.
5.
873cm
0.05L
1200kg
75dag
560dm
m
mL
mg
hg
km
Significant Figures
• Indicate the precision of a number
• Used for measurements
Rules for determining Sig Figs
1. All non-zero numbers are significant
2. Zeros sandwiched between significant
figures are always significant.
3. Zeros before the first non-zero number
are not significant. These zeros can be
thought of as “place holders”
4. Zeros at the end of a number are only
significant when they are decimals.
Atlantic – Pacific Rule
• If the decimal is Absent
in a measurement, start
on the Atlantic side (right
side of the number) with
the first nonzero digit. All
the preceding digits are
significant.
• If the decimal is Present
in a measurement, start
on the Pacific side (left
side of the number) with
the first nonzero digit. All
the following digits are
significant.
Sig Fig Practice
1.
2.
3.
4.
5.
6.
7.
803
60.56
5.780
0.0025
0.08150
200.
1.50 x 1021
Exact Numbers
• Exact numbers, such as the number of people in
a room, have an infinite number of significant
figures. Exact numbers are counting up how
many of something are present, they are not
measurements made with instruments. Another
example of this are defined numbers, such as 1
foot = 12 inches. There are exactly 12 inches in
one foot. Therefore, if a number is exact, it
DOES NOT affect the accuracy of a calculation
nor the precision of the expression. Some more
examples:
• There are 100 years in a century.
• 2 molecules of hydrogen react with 1 molecule
of oxygen to form 2 molecules of water.
Addition/Subtraction
• Round your final answer to the same
number of decimal places as the figure
with the least number of decimal places
Practice
1.
2.1 g
12.59 g
+ 34.73 g
2. 109.05 g
- 62.4 g
Multiplication/Division
• Round your final answer to the same
number of significant figures as the
number with the least number of significant
figures
Practice
2. The mass of a solid
1. 3.127
is 3.60g and its
x 8.01
volume is 1.8cm3.
What is the density of
the solid?
Scientific Notation
• Used as a shorthand for writing very small or very
large numbers
• Always written in the form a x 10b
 1  a < 10
 Exponent will be positive for numbers greater than 1
 Exponent will be negative for numbers less than 1
Practice
1.
2.
3.
4.
103,000
2 x 106
0.6842
8.56 x 10-4
=
=
=
=
Adding/Subtracting
• Must have the same exponent first! Change the
smaller exponent into the larger one
• Add/Subtract the non-exponent
• Keep the same exponent
Examples:
1. 2.7x103 + 3.2x102
2. 7.58x1020 – 6.2x1021
Multiplying/Dividing
•
•
Multiply/Divide non-exponent
Add/Subtract exponent
Examples:
• (7.2 x 10-2) (3.4 x 104) =
•
7.5 x 106 =
2.5 x 102
Percent Error
Measured – Accepted x 100
Accepted
* Also given on
Reference Table T
Example: Methyl alcohol boils at 65oC, a
student measures it to be 68oC. What is the
percent error?
Dimensional Analysis
•
•
•
You can multiply anything by 1 and not change
the value of the number
Multiplying by conversion factors is the same
as multiplying by 1
Just keep track of your units!!!!!
Examples:
1. How many seconds are there in 5.00 days?
2. Calculate the number of minutes in 2.0 years?
Express your answer in scientific notation.