Download Scientific Measurement

Scientific Measurement
1
Quantitative
vs. Qualitative
Qualitative measurement:
Descriptive
“This person feels feverish.”
Quantitative measurement:
Number + units
“This person has a
temperature of 102.3 F.”
2
Precise: how close a group of
measurements are.
Accurate: how close to the true
value a measurement is.
accurate
& precise
precise
only
neither
3
Precision vs. Accuracy ?
A student measured her
height to be 153, 155 and
156 cm.
Her true height is 168 cm.
Precise and/or accurate?
(Instruments are calibrated
to give accurate measurements)
4
Error
Student measures temperature
of boiling water to be 103.2oC.
The true value is 100.0oC.
Error
= measured - accepted
= 103.2oC – 100.0oC
= 3.2oC
5
Percent Error
error
x 100
Percent error =
accepted
oC
3.2
x
100
=
100oC
= 3.2%
6
Percent Error: Try It
A Quality Control technician
measures that there are
only 1.92 L of soda in a
bottle that should contain
2.00 L. What is the % error
in filling the bottle?
7
Scientific Notation
Avogadro’s Number:
602,200,000,000,000,000,000,000
6.022 x
23
10
Mass of H atom
0.00000000000000000000000166 g
1.66 x
-24
10 g
8
Scientific Notation
N. x
coefficient
6.02 x
m
10
exponent
23
10
9
Scientific Notation
1.Start with number in decimal form.
2.Count number of places to move
decimal point to get one digit to the
left of the decimal point.
•shift decimal left  exp. increases
•shift decimal right  exp. decreases
0.00083 = 8.3 x
-4
10
10
Scientific Notation: Try It !
Express in proper scientific notation:
2001.
0.00345
40230000.
5
34.5 x 10
-5
34.5 x 10
-6
0.029 x 10
11
Scientific Notation
Can you go backwards?
Express as decimal numbers.
3.3 x
-3
10
6.2 x
4
10
12
Using Scientific Notation
Multiplication (& division):
•multiply (divide) coefficients and
add (or subtract) exponents
(8.0 x
-2
10 )
x
5
(7.0 x 10 ) =
3
= 56 x 10
4
= 5.6 x 10
13
Using Scientific Notation
Try it !
(8.0 x
-2
10 )
 (7.0 x
5
10 )
=?
Note:
x divided by y:
xy
x/y
x
y
per
14
Using Scientific Notation
Addition & subtraction:
•convert to same exponents, then
just add (or subtract) coefficients
(3.42 x 10-5) - (2.5 x 10-6) =
(3.42 x
5
10 )
-5
10 )
- (0.25 x
=
-5
= 3.17 x 10
15
Using a Scientific
Calculator
(3.42 x 10-5) - (2.5 x 10-6) =
3.42E-5
-
Do not use the
2.5E-6
x
10
enter
button!
16
Scientific Notation Try It!
Try with & without scientific calc.
(6.2 x
-3
10 )
x (1.5 x
1
10 )
(8.8 x 106)  (2.2 x 10-1)
(6.7 x
-2
10 )
(7.32 x
+ (3.0 x
4
10 )
-3
10 )
– (6.10 x
3
10 )
17
Significant Figures
If I asked you to measure the
width of this room, how many
digits would you write down?
30 ft
32 ft
32.4 ft
32.43 ft
32.437 ft
18
Significant Figures:
--read the scale
--estimate one more digit
--always use units
0.6m
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0.61m
.
.
0.607m
.
.
19
Significant Figures
--read the scale
--estimate one more digit
--always use units
20
Reading Sig Fig: Rules

All non-zeros are significant.
1.234 ft

Zeros between non-zero
numbers are significant.
40,501 ft
21
Significant Figures

Zeros to the left of the first nonzero number are not significant.
0.00349 ft

Zeros to right of the last non-zero
number are significant if there
is a decimal point.
0.09030 ft
22
Significant Figures
300 ft
1 sig fig
300. ft
3 sig figs
How would you show 2 sig figs?
Need scientific notation:
3. x
1 sig fig
3.0 x 102 ft  2 sig figs
3.00 x 102 ft  3 sig figs
2
10 ft
23
“Exact” Numbers
(unlimited sig figs)
Counting: for example, 8 people
24
“Exact” Numbers
(unlimited sig figs)
Many conversion factors:
12 inches = 1 foot
12.000… in = 1.0000… ft
25
How Many Sig Figs ?
 123 m
 0.123 m
 40506 m
4
 9.800 x 10 m
 0.07080 m
 98000 m
 6 bottles
26
Rounding
If digit after the last sig fig is >5,
increase the last sig fig by 1.
32.6 to 2 sig figs is 33.
314.721
to 4 sig figs is ?
0.001775
to 2 sig figs is ?
9792
to 2 sig figs is ?
27
Sig Figs in Calculations
Addition & Subtraction: Sig figs of
answer determined by number with
fewest digits to right of decimal.
12.52
+ 349.0
361.52
28
Addition & Subtraction: Try It!
3.467 + 6.7 = ?
Honors:
(3.467 x 10-3) + (6.7 x 10-2) = ?
29
Sig Figs in Calculations
Multiplication & Division: Sig figs of
answer determined by number
with the least number of sig figs.
2.4526  8.3 = ?
= 0.295493976
= 0.30
30
Multiplication / Division: Try It!
(8.2 x 10-3) x (7.25 x 108) = ?
(6.234 x 10-5)  (4.3 x 10-2) = ?
31
Sig Figs in Calculations
With your backpack on,
your mass is 72.1 kg.
Your mass is 65.42 kg.
What is the mass of your
backpack?
32
Sig Figs in Calculations
How many fluid ounces are there
per glass if a 32 oz. soda bottle is
divided evenly among 7 glasses?
33
Metric (SI) Units
Add
9 3 in
8
+ 1 yd 2 ft
3
416
in
compared to:
Add 16.54 cm + 1.0160 m
Which is easier?
34
Metric System
Regents Table D
Quantity
Length
Volume
Mass
Temp
Time
Energy
Units
Meter
Cubic Meter, Liter
Gram, Kilogram
Kelvin, Celsius
Second
Joule
35
Prefixes (Regents Table C)
Prefix
Symbol
Factor
3
10
kilo
k
-1
deci
d
10
-2
centi
c
10
-3
milli
m
10
-6
micro
m
10
e.g. 1 cm = 10-2 m = 0.01 m
36
Prefixes (Regents Table C)
Write an equality for the
following units:
1 mm = ? m
4.3 cg = ? g
3 kg = ? g
6.9 ms = ? s
37
Metric Length
Unit
kilometer (km)
meter (m)
centimeter(cm)
millimeter (mm)
micrometer (mm)
Examples
~5/8 mile
~ yard
width of button
thickness of dime
diameter of cell
38
Metric Volume
Volume related to length:
(length3 = V)
Unit
Examples
Cubic centimeter
Cube of sugar
3
(cm = cc)
Liter (L)
Quart of milk
Milliliter (mL)
20 drops water
Note: 1cm3 = 1mL
39
Metric Mass
Unit
Examples
Kilogram (kg) Small textbook
Gram (g)
Paperclip
Milligram (mg) Ten grains of salt
1 mL = 1 cm3 = 1g H2O
40
Density
Sink or float?
Reading assignment handout.
41
Question ????
Which is heavier: a pound of lead
or a pound of feathers ?
vs.
?
42
Density
mass
Density = volume
Density of a substance is
independent of the mass
and volume.
Density of 2 kg of Pb is 11.4
Density of 9 kg of Pb is 11.4
3
g/cm
3
g/cm
43
Density
Density scale is defined by water.
Recall:
3
1 mL = 1 cm = 1g H2O
g
Thus DH2O = 1.00 3
cm
44
Density
Density in g/cm3 at 25oC
Au 19.3
Hg 13.5
Pb 11.4
Fe 7.87
Al
2.70
Bone 1.7-2.0
H2O
0.997
H2O
1.00 (4oC)
Ice
0.917 (0oC)
Gasoline 0.66-0.69
Wood
0.11-1.33
Air
0. 00119
45
Density
A plastic ball with a volume of 19.7
3
cm has a mass of 15.8 g.
Would this ball sink or float in a
container of gasoline?
3
(Density of gasoline is 0.68 g/cm .)
46
Temperature
Atoms & molecules
are always in motion.
Recall: temperature is
a measure of the average kinetic
energy of atoms & molecules.
47
Temperature
Is there a temperature where
motion stops ?
Yes! absolute zero
48
Temperature Scales
Water boils
Celsius
100
Water freezes
No motion -273
0
0
Kelvin
373
273
(Size of
degree is
the same)
49
Temperature Scales
Converting: Celsius
K=
Kelvin
oC
+ 273
Regents Table T
50
Temperature Scales
K=
oC
+ 273
Convert:
•25oC to K
•150K to oC
What is the difference between
the B.P. and F.P. of water in oC & in K?
51
Heat
Heat, a form of energy, flows
between two objects if they are at
different temperatures.
Hot
Cold
52
Heat
Heat (energy) is not
temperature (a measurement).
Which burns more: spoonful of
boiling water or pot of boiling water ?
53
54
Warm-up
Which is bigger?
102 or 103
-2
10
Note:
2
10
or
-3
10
=1x
2
10
55
Warm-up
Express in scientific notation:
0.000745
6,283,000,000
Do the following calculations:
6.2E-4 / 8.1E-3 =
7.1E-2 + 6.0E-3 =
Note: 6.2 x 10-4 = 6.2E-4
56
Warm-up
What are sig figs?
How many sig figs in:
0.090300 m?
42 sandwiches?
57
Warm-up
Do the calculation, express in proper
scientific notation and sig figs:
5.41cm + .27568 cm =
2.772E-2 cm / 8.1E3 cm =
Honors:
5.417E-2 cm + 2.7E-3 cm =
58
Warm-up
Do the calculation, express in proper
scientific notation and sig figs:
4.61 – 0.3472 =
6.77E-2 * 3.17841E3 =
How many meters are in 6.4 mm?
59
Warm-up
•How many grams are in 7.9 ng?
•What is the relationship between
volume in cm3, volume in mL,
and mass?
60