Transcript Significant Figures - Lompoc Unified School District

Mathematical Fundamentals
SI System
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Standard International System of
measurement – metrics
Has seven base units and many other
units derived from these seven
Seven Base Units
Quantity
Unit
length
mass
time
temperature
amount
current
intensity
meter
gram
second
kelvin
mole
ampere
candela
Abbreviation
m
g
s
K
mol
amp
cd
Derived Units
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Many other units are used in the metric
system, but they are combinations of the
base units
Volume
- volume = length x width x height
(m) x (m) x (m) = m3
- .001 m3 = 1 liter (L)
- 1 cm3 = 1ml
Prefixes
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Metric system utilizes prefixes which
indicate multiples of 10 of the unit
kilok
1000
hectoh
100
dekada
10
decid
.1
centic
.01
millim
.001
Converting Between Metric Units
3.65 dam = __________cm
2587 mm = __________hm
.0087 hl = __________cl
More Prefixes
TeraGigaMegaMicroNano Pico-
T
G
M
u
n
p
1012
109
106
10-6
10-9
10-12
Use the appropriate prefixes
3 x 106 L
15 x 10-9 g
8 x 108 m
3.5 x 10-6 A
1.46 x 1010 J
Temperature
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Metric unit – Kelvin – not used for
measurement
Measured in C (celsius)
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Old system is F (farenheit)
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K = C + 273.15
C = 5/9 (F -32)
What is 69 F in C and K?
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Temperature is an intensive property- does
not depend on the amount
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Extensive properties do depend on the
amount
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In the statement “a yellow sample is solid at
25 C. It weighs 6.0g and has a density of
2.3g/cm3” what are the intensive and
extensive properties?
Uncertainty
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We do not know infinite digits of a measurement
Exact numbers are known for sure
Inexact – have some question (estimates)
Precision and Accuracy
Accuracy refers to the agreement of a
particular value with the true value.
Precision refers to the degree of agreement
among several measurements made in the same
manner.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Reporting Numbers
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In recorded measurements, all the digits are
considered exact up until the last digit which
may be off by one
2.2405 ± .0001
All digits including the uncertain one are called
significant figures
We are fairly confident of these digits
Further uncertainty can be eliminated by
repeating the experiment
Which Digits Are Significant?
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Any non-zero number is significant
Any number to the left of a decimal is
significant
Zeros to the right of a decimal and behind
other numbers are significant
Zeros to the right of a decimal but in front
of other numbers are not significant
How many Significant Figures in
each below?
1)
2)
3)
4)
5)
6)
7)
8)
28.6
910
0.0076000
0.0144030
400
700.0
0.4004
1.30
3440.
10) 0.04604
11) 804.05
12) 1002
13) 400.
14) 0.000625000
15) 6000
16) 0.00067
9)
Round each to 3 Significant
Figures
1)
2)
3)
4)
5)
31.068
2.613
81.436
0.001567
1.1353
149.51
7) 6.561
8) 13.1252
9) 143.81
10) 0.000355
6)
Multiplying and Dividing
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Multiply or divide the number out as
normal but round the answer to the least
number of significant figures in the
problem
Solve each with correct Sig Figs
1)
2)
3)
4)
2.4 x 15.82 =
94.20  3.16722 =
(5.682 x 105) x (2.87 x 104) =
(2.145 x 10-5)  (6.75 x 104) =
Addition and Subtraction
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Add or subtract as normal but round the
answer with the same number of decimal
places as the quantity in the calculation
having the least
Solve each with correct Sig Figs
1)
2)
3)
4)
5.44 – 2.6103
2.099 + 0.05681
87.3 – 1.655
8.2 – 7.11
Conversions
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Often the units must be changed in order
to do a problem
Conversion factor method Is utilized
A26
Examples
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How many inches in 3.5 km?
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A chemical reaction produces 3.5 x 1025
atoms of product every hour. How many
will be produced in 2.5 hours?
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How many square cm in a square inch?
Density
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Identification tag for a substance
Every substance has a unique density
Mass
Density 
Volume
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The density of silver is 10.5 g/cm3. If 5.25g
of silver pellets are added to a graduated
cylinder containing 11.2 ml of water, to
what volume will the water rise?