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Significant Figures
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Recording a Measurement Using
Significant Digits:
When
recording a measurement,
include every digit that is absolutely
certain plus the first digit that must be
estimated (guessed). This is the
definition of a significant digit or
significant figure.
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Rules
The following rules are used to determine the
number of significant digits in a given
measurement.
1.
All non-zero digits are significant.
Ex: 374 (___ sig. figs)
8.1 (___ sig. figs)
2.
All zeroes between non-zero digits are
significant.
Ex: 50407 (___ sig. figs)
8.001 (___ sig. figs)
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Practice
Determine the number of sig. figs for the
following:
a)
2
b)
987
c)
56487209
d)
506973
e)
90003
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Rules con’t
3. Leading zeroes in a decimal are not significant.
Ex: 0.54 (__ sig figs)
0.0098 (__ sig figs)
4. Trailing zeroes are significant if they are to the
right of a decimal point.
Ex: 2370 (__ sig figs)
16000 (__ sig figs)
16000.0 (__ sig figs)
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Practice
 Determine
the number of sig. figs for each
value given.
a) 0.54 = __________ sig figs
b) 0.0098 = __________ sig figs
c) 2370 = __________ sig figs
d) 16070 = __________ sig figs
e) 160.0 = __________ sig figs
f) 37000 = __________ sig figs
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Rules con’t
5. *In numbers greater than 1, trailing zeroes
are not significant unless stated so.*
Ex: Determine the number of sig. figs.
a)Approximately
pep rally.
b)The
37000 students attended the
beaker contained 37000 grams of
Copper.
c)37000
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Scientific Notation
 The
last three zeroes may or may not be
part of the measurement. To show that they
are, we use scientific notation. All the zeroes
written in the number in scientific notation
are significant.
37000 with 3 sig. figs would be
37000 with 4 sig. figs would be
37000 with 5 sig. figs would be
37000 with 6 sig. figs would be
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Practice

Determine the number of sig. figs. for each
value given.
a) 5.80 x 104 =__________ sig figs
b) 4.6800 x 104 =__________ sig figs
c) 258000.0 =__________ sig figs
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Practice

Round each of the following to 3 sig figs
a) 5.8467 x 104
b) 458900
c) 258000.0
d) 784643
e) 45.097
f) 0.00086432
g) 0.06598
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Homework
 Significant
Figures Worksheet
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Trick: Pacific-Atlantic Rule
Here is an alternate rule for determining significant digits. The
rule is really a mnemonic device.You, the student, are easily
confused about the number of significant digits, especially if
zeroes are present. This rule will allow you to achieve success
in working with significant digits. This method is called the
”Pacific-Atlantic" method.
If the number in question does not contain a decimal, think
"A" for Absent. If the number in question does contain a
decimal, think "P" for Present.
Next, imagine a map of North America with north pointing to
the top of the page. The "A" now stands for Atlantic and the
"P" now stands for Pacific oceans.
Now, imagine an arrow starting from the correct coast being
drawn towards the number. Once the arrow hits a non-zero
digit, that digit and all digits after it are significant.
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Examples:

How many significant digits are shown in
the number?
a)37
500
b)0.040500
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Addition and Subtraction:
 General
Rules:
1. Add or subtract as normal.
2. Count the number of digits to the right of the
decimal.
3. The answer must be rounded to contain the same
number of decimal places as the value with the
LEAST number of decimal places. *If there are no
decimals then round to the number that is the least
accurate*
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Example: Perform the following
calculations.
a)
12.0 + 131.56 + 0.2798 =
b)
135 + 45 + 0.3804 =
c)
580 + 26.7 + 0.889 =
d)
1000 – 8900 + 98.8 =
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Multiplication and Division
 General
Rules:
1. Multiply or divide as normal.
2. Count the number of sig figs. to each number.
3. The answer must be rounded to contain the same
number of sig figs. as the number with the LEAST
number of sig figs.
Example 1. Perform the following calculation.
 51.3
x 13.75 = ?
Example 2.
 3.0×1012 ÷
6.02×1023 = ?
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Scientific Notation
 Expresses
numbers as a multiple of two
factors:
 a number between 1 and 10
 and ten raised to a power, or exponent.
 The
exponent tells you how many times the
first factor must be multiplied by 10
 (i.e. how many places to move the decimal
point, if there is no decimal point place it
at the end of the value)
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Convert into scientific notation
a) 1 392 000
b) 0.000 000 028
c) The mass of a proton is 0.000 000 000 000
000 000 000 000 001 672 62kg.
d) The mass of an electron is 0.000 000 000
000 000 000 000 000 000 000 910 939 kg.
 Why
do you think we use scientific notation?
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Multiplication and Division
using Scientific Notation
 Multiplication
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Multiply the first factors.
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Add the exponents.
a) (2 x 103) X (3 x 102) =
 Division
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Divide the first factors.
•
Subtract the exponents.
Dividend (top) – Divisor
(bottom)
b) (9 x 108) / (3 x 104) =
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Homework
Textbook
 Pg
32 #12-14
 Pg
33 #15, 16
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Homework
 Significant
Figures Review Worksheet
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Sig Figs Test