Scientific Notation to Standard Notation Positive and Negative Exponents.
Ch 8: Exponents E) Scientific Notation Objective: To simplify expressions involving scientific...
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Transcript of Ch 8: Exponents E) Scientific Notation Objective: To simplify expressions involving scientific...
Ch 8: ExponentsE) Scientific Notation
Objective:
To simplify expressions involving scientific notation.
Key concepts:
1. Write expressions in Standard Form
2. Write expressions in Scientific Notation
3. Multiply scientific notation expressions
4. Divide scientific notation expressions
Scientific Notationused to write very large or very small numbers expressed in the form:
Definitions
Standard FormAn expression written without exponents
€
a ×10b
a number between 1.0 and 9.9
an integer
Example 1
Example 2
12 jumps to the right3,780,000,000,000 =
€
3.78 ×1012
7 jumps to the left0.00000064 =
€
6.4 ×10−7
RulesFrom Standard Form to Scientific Notation
1) Determine where the decimal should be placed 2) Count how many places from the “new” decimal point to the “old” decimal pointTo the RIGHT = (+) positive exponent
To the LEFT = (−) negative exponent
11 jumps to the right
4 jumps left
7 jumps to the right
Classwork
46,000,000
620,000,000,000
0.000538
0.000004
=
€
4.6 ×107
=
€
6.2 ×1011
=
€
5.38 ×10−4
6 jumps left=
€
4 ×10−6
1)
2)
3)
4)
Example 1
Example 2
RulesFrom Scientific Notation to Standard Form
1) Move the current decimal point the number of places based on the exponent as follows:(+) positive exponent = to the RIGHT
(−) negative exponent = to the LEFT
08.43000000
€
3.6 ×105
€
8.43 ×10−7
3.60000 360,000
0.000000843
=
=
5)
6)
7)
8)
€
2.64 ×109
€
3.41×10−6
€
4 ×108
€
7 ×10−6
2.640000000 2,640,000,000
3.41000000 0.00000341
400000000 400,000,000
7000000 0.000007
Classwork
=
=
=
=
RulesMultiplying Scientific Notation expressions
1) Multiply the numbers that have no exponents.
2) Add the exponents to calculate the new exponent for 10.
3) Verify that the result is in scientific notation
€
a ×10b
a number between 1.0 and 9.9
an integer
€
(2.1×108 )(1.5 ×106 )
€
2.1×108 ×1.5 ×106
(2.1)(1.5)
€
×
€
(108 )(106 )
€
3.15 ×1014
Example 1
€
19.142 ×1015
1 jump right
€
(5.63×107)(3.4 ×108)
(5.63)(3.4)
€
×
€
(107 )(108 )
€
1.9142 ×1016
+1
Example 2
Not in Scientific Notation
3.15
€
× 108+6
19.142
€
× 107+8
smaller bigger
Classwork9)
€
(8 ×1014 )(1.2 ×1011 )
€
9.6 ×1025
10)
€
(2.4 ×107)(4.9 ×109 )
€
11.76 ×1016
€
1.176 ×1017
1 jump right
+1
11)
€
(3.7 ×1010)(6.5 ×108 )
€
24.05 ×1018
€
2.405 ×1019
1 jump right
+1
12)
€
(9.7 ×10−6 )(8.6 ×10−5)
€
83.42 ×10−11
1 jump right
+1
€
8.342 ×10−10
smaller bigger
smaller bigger
smaller bigger
RulesDividing Scientific Notation expressions
1) Divide the numbers that have no exponents.
2) Subtract the exponents to calculate the new exponent for 10.
3) Verify that the result is in scientific notation
€
a ×10b
a number between 1.0 and 9.9
an integer
Example 1 Example 2
€
9.1×1012
3.5 ×107
€
9.13.5
×1012
107
=
€
2.6 ×1012− 7
=
€
2.6 ×105
€
5.074 ×1023
5.9 ×1011
€
5.0745.9
×1023
1011
=
€
0.86 ×1023−11
=
€
0.86 ×1012
1 jump left
−1
=
€
8.6 ×1011
smallerbigger
13)
€
(8.88 ×1019)(3.7 ×105)
14)
€
5.589 ×1024
8.1×1012
€
2.4 ×1014
€
0.69 ×1012
€
6.9 ×1011
1 jump left
−1
=
€
8.883.7
×1019− 5
€
5.5898.1
×1024 −12
Classwork
=
=
smallerbigger