Transcript Slide 1

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Accuracy and Precision

Accuracy – how close a measured value is to the actual
(true) value

Precision – how close the measured values are to each other
Low Accuracy
Low Precision
Low Accuracy
High Precision
High Accuracy
High Precision
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Types of Error
 Random
Error – when you estimate a value to
obtain the last sig fig for any measurement
 Ex. Measuring the temperature to 1 decimal
place using a thermometer
 Systematic
Error – happens due to an inherent
error in the measuring system.
 Ex. using a worn metre stick to measure your
height
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Significant Figures

Significant figures : the “important” digits in a numerical
value.

the number contains all the digits that are certain plus one
digit that is uncertain.
Example: When a measurement is reported to be 47.5, that
means the 4 and 7 are the certain numbers and the 5 is the
uncertain numbers. It means that the actual value could be
any number between 47.4 – 47.6.
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Significant Figure Rules
Rule
Example
Significant
Figures
1. Nonzero digits are always
significant
1.254
4 sig. fig.
2. Leading zeros (zeros before
0.000124
any nonzero digits) are NOT
significant
3. Embedded zeros are
305.04
significant
3 sig. fig.
4. Zeros’ behind the decimal
point are significant
5 sig fig
124.00
5 sig. fig.
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State the number of significant
figures in each of the followings:
Measurement S.F.
a. 967
Measurement S.F.
e. 3.254
b. 1.034
f. 9.3
c. 1.010
g. 2.008
d. 5
h. 8.21
+ Rules for Sig Figs In Mathematical
Operations
 Multiplying
and Dividing Numbers
 In
a calculation involving multiplication or division,
the number of significant digits in an answer
should equal the least number of significant digits
in any one of the numbers being multiplied or
divided.

e.g. 9.0 x 9.0 =8.1 x 101, while 9.0 x 9 and 9 x 9
= 8 x 101
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Rules for Sig Figs In Mathematical
Operations
 Adding
and Subtracting Numbers
 When
quantities are being added or subtracted,
the number of decimal places (not significant
digits) in the answer should be the same as the
least number of decimal places in any of the
numbers being added or subtracted.

e.g. 2.0 + 2.03 = 4.0
Rules for Sig Figs In Mathematical
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Operations

Rounding Rules

1. If the digit after the one you want to keep is greater
than 5, then round up.
 e.g. To obtain 2 sig digs: 3.47 rounds to 3.5; 3.471 rounds
to 3.5

2. If the digit after the one you want to keep is less than
five, then do nothing.
 e.g. To obtain 2 sig digs: 3.44 rounds to 3.4; 3.429 rounds
to 3.4

3. If the single digit after the one you want is exactly 5,
round to the closest even number.
 e.g. To obtain 2 sig digs: 2.55 is rounded to 2.6; 2.25 is
rounded to 2.2 e.g. BUT, 2.251 is rounded to 2.3
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Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3
0.02 cm x 2.371 cm
0.04742 cm2
710 m ÷ 3.0 s
236.6666667 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
1.030 g ÷ 2.87 mL
2.9561 g/mL
23 m2
4.22 g/cm3
0.05 cm2
2.4 x 102 m/s
5.87 x 103 lb·ft
2.96 g/mL
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Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
+ Scientific Notation
A
method used to express really big or really small
numbers. Consist of two parts:
2.34 x 103
This number is
ALWAYS between
0 and 10
The 2nd part is always
10 raised to an
integer exponent
 The
first part of the number indicates the number of
significant figures in the value.
 The
second part of the number DOES NOT count
for significant figures.
How its Done
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 1. Place
the decimal point between the first and
second whole number, and write ‘x 10’ after the
number.
 e.g. For
12345, it becomes 1.2 x 10
 e.g. For 0.00012345, it also becomes 1.2 x 10
 2. Indicate
how many places you moved the
decimal by writing an exponent on the number 10.
a) A move to the left means a positive move.
 e.g. For
12345, it becomes 1.2 x 104
b) A move to the right means a negative move.
 e.g. For
0.00012345, it becomes 1.2 x 10-4
The Fundamental SI Units
+  In all sciences, calculations are done using SI units (Le
Système International d'Unités).
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The Fundamental SI Units
Physical
Quantity
Name
Abbr.
Length
meters
m
Time
second
s
Mass
kilogram
kg
Temperature
Kelvin
K
Amount of
Substance
Electrical
Charge
mole
Mol
Coulomb
C
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SI Prefixes

The international system of units consists of a set of units
together with a set of prefixes.
Prefix
Mega
Kilo
Deca
k
Hect
o
h
Symbol
M
Factor
106
103
102
101
base
(g, m, L)
da
100 = 1
Deci
Centi
Milli Micro
d
c
m

10-1
10-2
10-3
10-6
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Practice!
Original
Convert to…
Original
Convert to…
a) 3.15 m
cm e) 955g
kg
b) 20.0Mg
mg f) 178mm
cm
c) 75.4L
ml g) 650cm
mm
d)1350mL
L h)
s
88.74m
s
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Practice!
Original
a) 3.15 m
Convert to…
Original
315 cm e) 955g
Convert to…
0.955 kg
b) 20.0Mg
2.00 x 1010 mg f) 178mm
17.8 cm
c) 75.4L
0.0754 mL g) 650cm
6500 mm
Or 6.50X103 mm
d)1350mL
1.350 L h)
0.08874s
88.74m
s
Dimensional
Analysis
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 SAMPLE
PROBLEMS…
Convert 7 years to seconds.
REMEMBER: Set up conversion factors to get rid
of unneeded units, and to obtain needed units!
Conversion can be flipped if needed: 60 s = 1min =
60 s
1min
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