Chapter 2 Measurement and Problem Solving
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Transcript Chapter 2 Measurement and Problem Solving
Chapter 2
Measurement and
Problem Solving
What is a Measurement?
Quantitative
observation.
Comparison to an
agreed upon standard.
Every measurement has
a number and a unit.
Scientific Notation
Technique used to express very large or very
small numbers.
The sun’s
diameter is
1,392,000,000 m.
An atom’s
average diameter is
0.000 000 000 3 m.
Scientific Notation
Expresses a number as a product of a number
between 1 and 10 and the appropriate power
of 10.
The sun’s
diameter is
1.392 x 109 m.
An atom’s
average diameter is
3 x 10-10 m.
Scientific Notation
The number of places the decimal point is
moved determines the power of 10. The
direction of the move determines whether the
power of 10 is positive or negative.
Scientific Notation
If the decimal point is moved to the left, the
power of 10 is positive.
Sun’s diameter = 1,392,000,000 m = 1.392 x 109 m.
If the decimal point is moved to the right, the
power of 10 is negative.
Average atom’s diameter = 0.0000000003 m =
3 x 10-10 m.
Scientific Notation
1.
2.
3.
The World’s population is estimated to be
7,187,000,000 people. Express this number
in scientific notation.
Express the following numbers in scientific
notation: 0.0000671; 72.
Express the following numbers in standard
notation: 2.598 x 10-7; 9.5 x 104.
Significant Figures
Writing numbers to reflect precision.
All measurements have some degree of
uncertainty.
Significant Figures
Significant Figures
When writing measurements, all the digits
written are known with certainty except the
last one, which is an estimate.
45.872
Certain
Estimated
Record the certain digits and the first
uncertain digit (the estimated number).
Significant Figures
All non-zero digits are significant.
Interior zeros are significant.
1.5 has 2 significant figures.
1.05 has 3 significant figures.
Trailing zeros after a decimal point are
significant.
1.050 has 4 significant figures.
Significant Figures
Leading zeros are NOT significant.
0.001050 has 4 significant figures.
Zeros at the end of a number without a written
decimal point are ambiguous.
150 has 2 or 3 significant figures—
ambiguous.
Significant Figures
A number whose value is known with
complete certainty is exact.
Exact numbers have an unlimited number of
significant figures.
Significant Figures in Calculations
When multiplying or dividing measurements
with significant figures, the result has the
same number of significant figures as the
measurement with the fewest number of
significant figures.
5.02 × 89.665 × 0.10 = 45.0118 = 45
5.892 ÷ 6.10 = 0.96590 = 0.966
Significant Figures in Calculations
When rounding to the correct number of
significant figures, if the number after the
place of the last significant figure is:
0 to 4, round down.
5 to 9, round up.
In a series of calculations, carry the extra
digits through to the final result and then
round off.
Significant Figures in Calculations
When adding or subtracting measurements
with significant figures, the result has the
same number of decimal places as the
measurement with the fewest number of
decimal places.
5.74 + 0.823 + 2.651 = 9.214 = 9.21
4.8 - 3.965 = 0.835 = 0.8
Significant Figures in Calculations
1.
2.
An impossibly regular, paved walkway mysteriously appears
overnight; leading out of Seattle. Careful measurement
shows this walkway to be 15,432 meters long and 0.42
meters wide. To the correct number of significant figures,
what area is covered by walkway? How would this number
change if the walkway were 0.41 meters wide? 0.43 meters
wide?
By the next morning, this walkway has grown 0.42 meters.
To the correct number of significant figures, how long is it
now?
Units of Measurement
Units tell the standard quantity to which we
are comparing the measured property.
Scientists use a set of standard units for
comparing all our measurements.
Units of Measurement
The SI System
Quantity
Length
Unit
meter
Symbol
m
Mass
kilogram
kg
Time
second
s
Temperature
kelvin
K
Units of Measurement
Length
Measure of the two-dimensional distance an
object covers.
Units of Measurement
Mass
Measure of the amount
of matter present in an
object.
Weight: measure of the
gravitational pull on an
object.
Units of Measurement
All units in the SI system are related to the
standard unit by a power of 10.
The power of 10 is indicated by a prefix.
Units of Measurement
Prefix
Symbol
Decimal
Equivalent
Power of 10
1,000,000
Base x 106
1,000
Base x 103
mega-
M
kilo-
k
deci-
d
0.1
Base x 10-1
centi-
c
0.01
Base x 10-2
milli-
m
0.001
Base x 10-3
micro-
m
0.000 001
Base x 10-6
nano-
n
0.000 000 001
Base x 10-9
Units of Measurement
Volume
Measure of the
amount of 3-D
space occupied by
a substance—a
derived unit.
Unit Conversions
Dimensional analysis: using units as a guide
to problem solving.
A quantity in one unit is converted to an
equivalent quantity in a different unit by using a
conversion factor that expresses the relationship
between units.
Unit Conversions
1.
2.
A golfer putted a golf ball 6.8 ft across a
green. How many inches does this represent?
How many centimeters?
What is the volume of a 1.25 gallon jug in
cubic centimeters? Cubic inches?
(1 gal = 4 qts; 1 L = 1.057 qts)
Density
Mass of substance per unit volume of the
substance.
Mass
Density
Volume
Density
Volume vs. Mass of Brass
y = 8.38x
160
140
Mass, g
120
100
80
60
40
20
0
0.0
2.0
4.0
6.0
8.0
10.0
Volume, cm3
12.0
14.0
16.0
18.0
Density
Volume of a solid can be determined by water
displacement.
Density
Density :
solids > liquids > gases
Density
1.
2.
3.
A certain mineral has a mass of 17.8 g and a volume
of 2.35 cm3. What is the density of this mineral?
What is the mass of a 49.6 mL sample of a liquid,
which has a density of 0.85 g/mL?
Copper has a density of 8.96 g/cm3. If 75.0 g of
copper is added to 50.0 mL of water in a graduated
cylinder, to what volume reading will the water level
in the cylinder rise?
Density
Summary of Topics: Chapter 2
Scientific notation
Significant figures
Exact numbers, Measured numbers
Metric units, prefixes
Difference between mass and weight
Conversion factors
Density; D = m/v