Transcript Measurements

Significant Figures
Integrated Science
Dr. May
Significant Figures
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Numbers obtained from measurements are
never exact values
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Maximum precision includes all digits that
are known plus one estimated
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The digits used to express a measured
quantity are known as significant figures
Evaluating Zero
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In any measurement all nonzero numbers
are significant
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65.6291 grams has six significant figures
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Zeros may or may not be significant
depending on their position in the number
Zero is Significant When
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It is between nonzero digits
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2.05 has three significant figures
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61.009 has five significant figures
Zero is Significant When
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It is at the end of a number that includes a
decimal point
0.500 has three significant figures
 25.160 has five significant figures
 200. has three significant figures
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Zero is Not Significant When
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It comes before the first nonzero digit
(These zeros are used to place the decimal)
0.0025 has two significant figures
 0.00708 has three significant figures
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Zero Is Not Significant When
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It comes at the end of a number that
contains no decimal point
1000 has one significant figure
 590 has two significant figures
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Determine Significant Figures
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4.5 inches
3.025 feet
125.0 meters
0.001 miles
25.0 grams
100,000 people
205 birds
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4
4
1
3
1
3
Rounding Off Numbers
Integrated Science
Dr. May
Rounding Off Numbers
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When we do calculations we often obtain
answers with more digits than are justified
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We need to drop the excess digits to express
the answer in the proper number of
significant figures
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This is called rounding off numbers
Rounding Off Numbers - Rule 1
When the first digit after those you want to
retain is 4 or less, that digit and all others to
the right are dropped.
 The last digit retained is not changed
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Round 1.00629 to 4 significant figures
 1.00629 = 1.006
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Rounding Off Numbers - Rule 2
When the first digit after those you want to
retain is 5 or greater, that digit and all others
to the right are dropped.
 The last digit retained is increased by 1
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Round 18.02500 to four significant figures
 18.02500 = 18.03
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Round Off As Indicated
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42.246 (four)
88.015 (four)
0.08965 (three)
0.08965 (two)
225.3 (three)
14.150 (three)
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42.25
88.02
0.0897
0.090
225
14.2
Scientific Notation
Integrated Science
Dr. May
Scientific Notation
Very large and very small numbers can be
simplified and conveniently written using a
power of 10
 4,500,000,000 (4.5 billion) can be written
4.5 x 109
 Writing a number as a power of 10 is called
scientific notation
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Powers of Ten
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100
101
102
103
104
105
106
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10
100
1,000
10,000
100,000
1,000,000
Negative Powers of Ten
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10 0
10 1
10 2
10 3
10 4
10 5
10 6
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0.1
0.01
0.001
0.0001
0.00001
0.000001
Number to Scientific Notation
Convert 0.000056 to 5.6 x 10 5
 Choose the number between 1 and 10 = 5.6
 Multiply by 10: 5.6 x 10
 If the number is < 1 use a negative exponent
5.6 x 10 
 Count the spaces the decimal was moved
5.6 x 10 5
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Number to Scientific Notation
Convert 560,000 to 5.6 x 10 5
 Choose the number between 1 and 10 = 5.6
 Multiply by 10: 5.6 x 10
 If the number is > 1 use a positive exponent
5.6 x 10
 Count the spaces the decimal was moved
5.6 x 10 5
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Scientific Notation to Number
Convert 5.6 x 10 5 to 560,000
 Write the significant figures = 56
 The exponent is positive, the number is > 1
 Add zeros to place the decimal 5 spaces
to the right
560,000.
 5 
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Scientific Notation to Number
Convert 5.6 x 10 5 to 0.000056
 Write the significant figures = 56
 The exponent is negative, the number is < 1
 Add zeros to place the decimal 5 spaces
to the left
0.000056
 5 
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Convert To Scientific Notation
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0.00034
0.00145
0.0000985
0.016856
0.0003967
0.0000002
0.00040
0.00600
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3.4 x 10 4
1.45 x 10 3
9.85 x 10 5
1.6856 x 10 2
3.967 x 10 4
2 x 10 7
4.0 x 10 4
6.00 x 10 3
Convert To Scientific Notation
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3400
36,000,000
367,800,000,000
58
65789
1,000,000,000
2,000
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3.4 x 103
3.6 x 107
3.678 x 1011
5.8 x 101
6.5789 x 104
1 x 109
2 x 103
Convert to Numerical Values
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7.4 x 103
5.6 x 105
6.674 x 1010
5.1 x 104
6.5559 x 101
3.64186 x 104
1 x 103
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7,400
560,000
66,740,000,000
51,000
65.559
36,418.6
1,000
Convert to Numerical Values
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7.4 x 103
5.6 x 105
6.674 x 108
5.1 x 104
6.5559 x 101
3.641 x 104
1 x 103
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0.0074
0.000056
0.00000006674
0.00051
0.65559
0.0003641
0.001
The End
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This presentation was created for the benefit
of our students by the Science Department
at Howard High School of Technology
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Please send suggestions and comments to
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