Transcript Measure
Significant Figures
Chemistry
Dr. May
Significant Figures
Numbers obtained from measurements are
never exact values
Maximum precision includes all digits that
are known plus one estimated
The digits used to express a measured
quantity are known as significant figures
Evaluating Zero
In any measurement all nonzero numbers
are significant
65.6291 grams has six significant figures
Zeros may or may not be significant
depending on their position in the number
Zero is Significant When
It is between nonzero digits
2.05 has three significant figures
61.009 has five significant figures
Zero is Significant When
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
Zero is Not Significant When
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
Zero Is Not Significant When
It comes at the end of a number that
contains no decimal point
1000 has one significant figure
590 has two significant figures
Determine Significant Figures
4.5 inches
3.025 feet
125.0 meters
0.001 miles
25.0 grams
100,000 people
205 birds
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2
4
4
1
3
1
3
Rounding Off Numbers
Chemistry
Dr. May
Rounding Off Numbers
When we do calculations we often obtain
answers with more digits than are justified
We need to drop the excess digits to express
the answer in the proper number of
significant figures
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
Round 1.00629 to 4 significant figures
1.00629 = 1.006
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
Round 18.02500 to four significant figures
18.02500 = 18.03
Round Off As Indicated
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
Chemistry
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
Powers of Ten
100
101
102
103
104
105
106
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1
10
100
1,000
10,000
100,000
1,000,000
Negative Powers of Ten
10 0
10 1
10 2
10 3
10 4
10 5
10 6
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1
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
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
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
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
Convert To Scientific Notation
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
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
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
7.4 x 103
5.6 x 105
6.674 x 108
5.1 x 104
6.5559 x 101
3.641 x 104
1 x 103
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0.0074
0.000056
0.00000006674
0.00051
0.65559
0.0003641
0.001
The End
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at Howard High School of Technology
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