Significant Figures

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Scientific Notation,
Significant Figures
and Metric
9/10/14
Scientific Notation
 The components of scientific notation:
8.238 x 10-31
 “8.238” is the coefficient
 “x 10” is the base
 “-31” is the exponent
 Where the coefficient has to be a number:
1 ≤ coefficient < 10
Significant Figures
 Significant Figures (sig. figs.): the number of
digits that carry meaning contributing to the
precision of a measurement or calculated
data.
Precision and Accuracy
Low Accuracy
High Precision
High Accuracy
Low Precision
High Accuracy
High Precision
Significant Figures
 Each recorded measurement has a certain
number of significant figures.
 Calculations done on these measurements
must follow the rules for significant figures.
 Placeholders, or digits that have not been
measured or estimated, are not considered
significant.
Significant Figures
 There are 5 rules to determine which zeros in
a number are significant or not.
Rules for Significant Figures
 Rule #1: All non-zero digits (1-9) are
significant.
For example:
453
number of sig figs______
345.21 number of sig figs______
Rules for Significant Figures
 Rule #2: Zeroes between non-zero digits are
significant.
For example:
12.007
number of sig figs______
2014
number of sig figs______
Rules for Significant Figures
 Rule #3: If a number ends in zeroes, the
zeroes to the right are NOT significant IF
there is NO decimal point present.
For example:
47100
number of sig figs______
20060
number of sig figs______
40000
number of sig figs______
Rules for Significant Figures
 Rule #4: Zeroes to the left of the first non-
zero digit are NOT significant.
For example:
1.02
0.12
0.00127
0.00040301
number of sig figs______
number of sig figs______
number of sig figs______
number of sig figs______
Rules for Significant Figures
 Rule #5: If a number ends in zeroes to the
right of the decimal point, those zeroes are
significant.
For example:
 2
number of sig figs______
2.0
number of sig figs______
2.00
number of sig figs______
2.000
number of sig figs______
{This signifies greater precision.}
The Atlantic - Pacific Rule
for Significant Figures
 When determining the number of significant
figures ask the question:
 “Does the number have a decimal point?”
(YES or NO answer)
 If YES, then think of “P” for Present and the
Pacific ocean
 If NO, then think of “A” for Absent and the
Atlantic ocean
The Atlantic and Pacific Rule
for Significant Figures
The Atlantic and Pacific Rule
for Significant Figures
 "P" for "Present". This means that we imagine an
arrow coming in from the Pacific ocean, from the
left side
 "A" for "Absent". This means that we imagine an
arrow coming in from the Atlantic ocean, the right
side.
The Atlantic and Pacific Rule
for Significant Figures
 Look for the first non zero number starting
from that direction
 That number, and all other numbers following
it are considered to be significant
 For “P” the numbers to the right of the first
non zero number
 For “A” the numbers to the left of the first
non zero number
Examples
1) 0.020110
2) 730800
3) 3300
4) 3300.0
Rounding Sig. Figs.
Rounding Sig. Figs.
 The goal is to round the number to
the appropriate amount of sig. figs.
without changing the value too much.
Rounding Calculations
 For multiplication and division:
 Round to the number that has the least
amount of sig. figs.
 Note: There are different rules for addition
and subtractions
Rounding Sig. Figs.
 Look at the left most non-zero numbers to identify
the ones that you will keep
 If the number to the right of the last digit is 5 or
higher round up, 4 or lower round down
 LEFT of Decimal: Replace non significant
figures with zeroes if they are to the LEFT of the
decimal point
 RIGHT of Decimal: Drop non significant figures
if they are to the RIGHT of the decimal point
Examples in Your Notes
 1) 43252202 to 3 sig figs

43252202 (5 = 5 so round up and replace
non sig. figs. with zeros)

43300000
 2) 0.0073384658419 to 4 sig figs

0.0073384658419 (4 < 5 so round down and
drop non sig. figs.)

0.007338
Examples in Your Notes
 3) 47.66666667 to 5 sig figs

47.66666667 (6 > 5 so round up and drop non
sig. figs.)

47.667
 4) 794951.741583 to 2 sig figs

794951.741583 (4 < 5 so round down and
replace non sig. figs. with zeroes AND drop non
sig. figs. to the right of the decimal)

790000
Rounding Calculations
Examples
1. 5.50 × 2.00
2. 2.437 × 10-12 / 4.5 × 1014
Rounding Calculations
Examples
1. 5.50 × 2.00
Calculator reads “11”
Answer is 11.0
2. 2.437 × 10-12 / 4.5 × 1014
Calculator reads “5.415555556E-27”
Answer is 5.4 × 10-27
Lab Rubric
 1st column “Self Evaluation”
 2nd column “Peer Evaluation” (student initials)
 3rd column “Self Evaluation #2”
 4th column “Teacher Evaluation”
Metric Units (base unit)
Quantity
Base Unit
Symbol
Length
Meter
m
Mass
Gram
g
Time
Second
s
Volume
Liter
L
Force
Newton
N
Energy
Joule
J
Metric Prefixes
*Learn highlighted ones!
Prefix
Prefix Symbol
Multiplier
mega-
M
106 (1000000)
kilo-
k
103 (1000)
BASE UNIT
-
100 (1)
centi-
c
10-2 (0.01)
milli-
m
10-3 (0.001)
micro-
μ
10-6 (0.000001)
Extra Practice
Sig. Figs. Practice
Ex 1) 0.020110
Ex 2) 730800
 1) 48001
 2) 9807000
 3) 0.008401
 4) 40.500
 5) 64000
 6) 64000.
 7) 64000.00
 8) 0.0107050
Sig. Figs. Practice
Ex 1) 0.020110
Ex 2) 730800
 1) 48001
 2) 9807000
 3) 0.008401
 4) 40.500
 5) 64000
 6) 64000.
 7) 64000.00
 8) 0.0107050
Ex 1) 0.020110 (5 sig. figs.)
Ex 2) 730800 (4 sig. figs)
 1) 48001 (5 sig. figs.)
 2) 9807000 (4 sig. figs.)
 3) 0.008401 (4 sig. figs.)
 4) 40.500 (5 sig. figs.)
 5) 64000 (2 sig. figs.)
 6) 64000. (5 sig. figs.)
 7) 64000.00 (7 sig. figs.)
 8) 0.0107050 (6 sig. figs.)
Rounding Practice
1. 0.0018563333 to 3 sig. figs.
2. 34498221 to 2 sig. figs.
3. 4781.2233 to 3 sig figs.
4. 568.7893201 to 5 sig. figs.
5. 67488133 to 1 sig. fig.
6. 0.0219999 to 2 sig. figs.
7. 4.7004021 to 4 sig. figs.
8. 998701 to 1 sig. fig.
Rounding Practice
1. 0.0018563333 to 3 sig. figs.
1. 0.00186
2. 34498221 to 2 sig. figs.
2. 34000000
3. 4781.2233 to 3 sig figs.
3. 4780
4. 568.7893201 to 5 sig. figs.
4. 568.79
5. 67488133 to 1 sig. fig.
5. 70000000
6. 0.0219999 to 2 sig. figs.
6. 0.022
7. 4.7004021 to 4 sig. figs.
7. 4.700
8. 998701 to 1 sig. fig.
8. 1000000
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