Download Using Scientific Measurements - Belle Vernon Area School District

Using Scientific Measurements
2.3
Objective/Warm-Up
• SWBAT identify and calculate significant
figures and use scientific notation.
• What is the correct
measurement for
this buret?
4.85 mL
Notes-Accuracy
Word/Phrase:
accuracy
Hints or diagram:
Definition:
How close the
measurement is to
the real, true, or
correct value
Meaning in My own
words:
Notes-Precision
Word/Phrase:
precision
Hints or diagram:
Definition:
How close measurements
are to each other
Meaning in My own words:
Add your own
• What would a picture look like that is neither
precise nor accurate?
Objective/Warm-Up
• SWBAT review dimensional analysis,
density, and metric conversions.
• Record the measurement for each cylinder.
Significant Figures
• Sig figs – all the digits known with
certainty plus one final digit, which is
somewhat estimated or uncertain
• Graduated cylinder example
• 42.5 mL - the 5 is the estimated
number
Rules for Determining Sig. Figs.
• All non zero digits are significant
• Zeros at the end only count if there is
a decimal point
• Decimal = go to 1st non zero and
count everything to the right
• Exact numbers have infinite
significant figures (1m = 1000mm)
• Calculators exaggerate precision
Sig. Fig Examples
•
•
•
•
•
•
How many sig figs are in…
203000
1000.00
0.00052
0.06400
79.810
Significant Digits
Number # of
Sig
Figs
6.751 g
Number
# of
Sig
Figs
Number
# of
Sig
Figs
4
30.07 g
4
4
0.157
kg
28.0
mL
2500 m
3
0.106 cm
3
3
0.0067 g
2
54.52
cm3
0.1209
m
2.690 g
3
2
43.07
cm
1000 m
4
0.070 g
0.0230
cm3
26.509
cm
2
5
4
4
1
Objective/Warm-Up
• SWBAT review conversions and SI units.
• What is the measurement shown in the
graduated cylinder?
• How many significant figures in these
numbers?
–5.0070
–3.4000
–3500
–0.00120
–0.07070
Objective/Warm-Up
• SWBAT accurately and precisely measure
volume and calculate using scientific notation.
How many sig figs are in…
• 203000
• 1000.00
• 0.00052
• 0.06400
• 79.810
Significant Figures
• Multiplication and division sig. figs =
answer has no more figs. than the
msmt. with the least # of sig. figs.
12.257 5 #’s
x 1.162 4 #’s
14.2426340
4 #’s = 14.24
Multiply/Divide with Sig Figs
• Your answer must have the same number
of sig figs as the measurement with the
fewest number of sig figs.
Calculate the volume if L = 3.65 cm, W =
3.20 cm, and H = 2.05 cm
V = 23.944 cm3,
after rounding to the correct number of
sig figs, V=23.9 cm3
Significant Figures
• Addition and subtraction = answer has
no more numbers to the right of the
decimal pt. than the number with the
least numbers to the right of the
decimal.
3.9 5
2.8 79
+ 213.6
220.4 29
= 220.4
Addition/Subtraction with Sig Figs
• Your answer must have the same number
of decimal places as the value with the
fewest decimal places
28.0 + 23.538 + 25.68 =
77.218
Round so that the answer is 77.2
Check-Up
• How can we judge accuracy?
• How can we judge precision?
• How do accuracy and precision relate to
measurement?
Objective/Warm-Up
• Students will be able to use significant digits
and scientific notation in calculations.
• Warm-Up: Section Review Worksheet
Scientific Notation
• 29640000000000000000000
copper atoms in 1 penny
• 2.964 x 1022 atoms
• 2 Parts to scientific notation
1. # between 1 and 10
2. Power of 10
Scientific Notation
• We use the idea of exponents to make it easier to
work with large and small numbers.
• 10,000 = 1 X 104
• 250,000 = 2.5 X 105
• Count places to the left until there is one number to
the left of the decimal point.
• 230,000 = ?
• 35,000 = ?
Scientific Notation Continued
• 0.00006 = 6 X 10-5
• 0.00045 = 4.5 X 10-4
• Count places to the right until there is one number to the
left of the decimal point
• 0.003 = ?
• 0.0000025 = ?
Scientific Notation Examples
Change from scientific notation
a) the distance from Pluto to the Sun is 5.9×10 12 meters
b) the Milky Way disk radius is 3.9×1020 meters.
c) The speed of light is 3 x 10 8 meters/second.
d) the sun is 1.5x 1011 meters from earth
e) Mass of proton : 1.6726 x 10-27 kg
f) Mass of neutron: 1.6749 x 10-27 kg
g) Mass of electron: 9.10939 × 10-31 kg
Change into scientific notation
h) 0.000 000 000 753 kg is the mass of a dust particle
i) A proton has a diameter of approximately 0.000000000001 mm
Positive Exponents
•
•
•
•
101 = 10
102 = 10X10= 100
103 = 10X10X10 = 1000
104 = 10X10X10X10 = 10,000
Negative Exponents
•
•
•
•
10-1 = 1/10 = 0.1
10-2 = 1/100 = 0.01
10-3 = 1/1000 = 0.001
10-4 = 1/10000 = 0.0001
Quick Review
• When multiplying:
– Add the exponents
• When dividing:
– Subtract the exponents
Multiplying with Scientific Notation
• Add the Exponents
• 102 X 103 = 105
• 100 X 1000 = 100,000
Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103)
• 230 X 3300
• Multiply the Coefficients
• 2.3 X 3.3 = 7.59
• Add the Exponents
• 102 X 103 = 105
• 7.59 X 105, round to 7.6 x 105
Multiplying with Scientific Notation
• (4.6 X 104) X (5.5 X 103) = ?
• (3.1 X 103) X (4.2 X 105) = ?
Dividing with Scientific Notation
• Subtract the Exponents
• 104/103 = 101
• 10000/ 1000 = 10
Dividing with Scientific Notation
•
•
•
•
•
•
•
(3.3 X 104)/ (2.3 X 102)
33000 / 230 = 143.4783
Divide the Coefficients
3.3/ 2.3 = 1.434783
Subtract the Exponents
104 / 102 = 102
1.4347823 X 102, round to 1.4 x 102
Dividing with Scientific Notation
• (4.6 X 104) / (5.5 X 103) = ?
• (3.1 X 103) / (4.2 X 105) = ?
Wrap-Up
• Summarize the rules for multiplying and
dividing in scientific notation.
• Why do we use scientific notation?
Scientific Notation
•
•
•
•
•
•
•
0.000000000000003332 kg
3.332 x 10-15 kg
1970000000 L
1.97 x 109
What is ….. In scientific notation?
4.58 x 105
9.05 x 10-3