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03/07/0103/07/01 Lecture 22Lecture 22 11
Unit 3 Lecture 22Unit 3 Lecture 22Negative ExponentsNegative Exponents
Negative ExponentsScientific Notation
03/07/0103/07/01 Lecture 22Lecture 22 22
• To evaluate exponential expressions with To evaluate exponential expressions with negative exponentsnegative exponents
• To write number in scientific notationTo write number in scientific notation
• To convert numbers in scientific notation to To convert numbers in scientific notation to decimal formdecimal form
ObjectivesObjectives
03/07/0103/07/01 Lecture 22Lecture 22 33
33-4-4 means means 1/1/ 3344
bb-n-n means means 1/ b1/ bnn
n-n 1 1b = =
b b b b ... b
4-4 1
.01234581
1 1= =3 3 33
33
Raising a Number to a Negative PowerRaising a Number to a Negative Power
03/07/0103/07/01 Lecture 22Lecture 22 44
To raise a number to a negative power use the ^ key, and (-) key
Use of the calculator to Use of the calculator to evaluate an exponential evaluate an exponential expression.expression.
33-4 -4 is keyed in as is keyed in as
33,, ^̂,, (-) (-),, 4 4, , ENTERENTER
.01235.01235
03/07/0103/07/01 Lecture 22Lecture 22 55
Use a CalculatorUse a Calculator
ExpressionExpression EvaluationEvaluation
88-2 -2 ==
-6-6-4 -4 ==
(-6)(-6)-4 -4 ==
.08.08-5 -5 ==
03/07/0103/07/01 Lecture 22Lecture 22 66
Use a CalculatorUse a Calculator
ExpressionExpression EvaluationEvaluation
88-2 -2 == .015625.015625
-6-6-4 -4 ==
(-6)(-6)-4 -4 ==
.08.08-5 -5 ==
03/07/0103/07/01 Lecture 22Lecture 22 77
Use a CalculatorUse a Calculator
ExpressionExpression EvaluationEvaluation
88-2 -2 == .015625.015625
-6-6-4 -4 == -.000771605-.000771605
(-6)(-6)-4 -4 ==
.08.08-5 -5 ==
03/07/0103/07/01 Lecture 22Lecture 22 88
Use a CalculatorUse a Calculator
ExpressionExpression EvaluationEvaluation
88-2 -2 == .015625.015625
-6-6-4 -4 == -.000771605-.000771605
(-6)(-6)-4 -4 == .000771605.000771605
.08.08-5 -5 ==
03/07/0103/07/01 Lecture 22Lecture 22 99
Use a CalculatorUse a Calculator
ExpressionExpression EvaluationEvaluation
88-2 -2 == .015625.015625
-6-6-4 -4 == -.000771605-.000771605
(-6)(-6)-4 -4 == .000771605.000771605
.08.08-5 -5 == 305,175.7812305,175.7812
03/07/0103/07/01 Lecture 22Lecture 22 1010
Find the monthly payments on a 48-month car loan of $18,000 at 3% annual interest.
P = Monthly paymentP = Monthly paymentA = Amount of loanA = Amount of loan i = Interest rate per monthi = Interest rate per monthn = Number of paymentsn = Number of payments -n
iP=A1- 1+i
.03/12 = .0025; interest rate per month
-48.0025P=18000
1- 1+.0025
03/07/0103/07/01 Lecture 22Lecture 22 1111
Find the monthly payments on a 48-month car loan of $18,000 at 3% annual interest.
-481+.00
.0025P=180025
01-
..0025P88705
=180001-
.11.0025P=18000
295
03/07/0103/07/01 Lecture 22Lecture 22 1212
Find the monthly payments on a 48-month car loan of $18,000 at 3% annual interest.
-481+.00
.0025P=180025
01-
..0025P88705
=180001-
.11295.0025P=18000 18000(.022133)
P=$398.39 per month
03/07/0103/07/01 Lecture 22Lecture 22 1313
Clintons can afford a $1000 monthly house payment at 7.2% annual interest rate for 360 months. How expensive a house can they afford?
-360.0061000=A
1- 1+.006
-niP=A
1- 1+i
P = Monthly paymentP = Monthly paymentA = Amount of loanA = Amount of loan i = Interest rate per monthi = Interest rate per monthn = Number of paymentsn = Number of payments
.072/12 = .006; interest rate per month
03/07/0103/07/01 Lecture 22Lecture 22 1414
Clintons can afford a $1000 monthly house payment at 7.2% annual interest rate for 360 months. How expensive a house can they afford?
-3601+.006
.0061000=A1-
.11.0061000=A
1- 607
.8839.0061000=A .0067879
3
1000 =$147,320.97
.0067879A
03/07/0103/07/01 Lecture 22Lecture 22 1515
A number in Scientific Notation has the form A number in Scientific Notation has the form P x 10P x 10nn where 1 where 1<<P<10 and n is an integer.P<10 and n is an integer.
8,200,000 = 8,200,000 =
Scientific NotationScientific Notation
88..20 x 1020 x 1066 88.. 200000 200000..
03/07/0103/07/01 Lecture 22Lecture 22 1616
A number in Scientific Notation has the form A number in Scientific Notation has the form P x 10P x 10nn where 1 where 1<<P<10 and n is an integer.P<10 and n is an integer.
8,200,000 = 8,200,000 =
Scientific NotationScientific Notation
88..20 x 1020 x 1066 88.. 200000 200000..
03/07/0103/07/01 Lecture 22Lecture 22 1717
A number in Scientific Notation has the form A number in Scientific Notation has the form P x 10P x 10nn where 1 where 1<<P<10 and n is an integer.P<10 and n is an integer.
.000517 = .000517 =
Scientific NotationScientific Notation
55..17 x 1017 x 10-4-4 ..00050005..1717
03/07/0103/07/01 Lecture 22Lecture 22 1818
A number in Scientific Notation has the form A number in Scientific Notation has the form P x 10P x 10nn where 1 where 1<<P<10 and n is an integer.P<10 and n is an integer.
7, 300, 000 7, 300, 000
Scientific Form to Decimal FormScientific Form to Decimal Form
77..3 x 103 x 1066 77..300000300000..
77..3 x 103 x 1066 = =
03/07/0103/07/01 Lecture 22Lecture 22 1919
A number in Scientific Notation has the form A number in Scientific Notation has the form P x 10P x 10nn where 1 where 1<<P<10 and n is an integer.P<10 and n is an integer.
.0003141 .0003141
Scientific Form to Decimal FormScientific Form to Decimal Form
33..141 x 10141 x 10-4-4 ..00030003..141141
33..141 x 10141 x 10-4-4 = =
03/07/0103/07/01 Lecture 22Lecture 22 2020
A number in Scientific Notation has the form A number in Scientific Notation has the form P x 10P x 10nn where 1 where 1<<P<10 and n is an integer.P<10 and n is an integer.
.000517 = .000517 =
Scientific NotationScientific Notation
55..17 x 1017 x 10-4-4 ..00050005..1717
03/07/0103/07/01 Lecture 22Lecture 22 2121
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = =
4.18 x 104.18 x 10-4 -4 ==
7.86 x 107.86 x 108 8 ==
8.673 x 108.673 x 10-10 -10 ==
3.3 x 103.3 x 10-2 -2 ==
03/07/0103/07/01 Lecture 22Lecture 22 2222
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 ==
7.86 x 107.86 x 108 8 ==
8.673 x 108.673 x 10-10 -10 ==
3.3 x 103.3 x 10-2 -2 ==
03/07/0103/07/01 Lecture 22Lecture 22 2323
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 == .000418.000418
7.86 x 107.86 x 108 8 ==
8.673 x 108.673 x 10-10 -10 ==
3.3 x 103.3 x 10-2 -2 ==
03/07/0103/07/01 Lecture 22Lecture 22 2424
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 == .000418.000418
7.86 x 107.86 x 108 8 == 786,000,000786,000,000
8.673 x 108.673 x 10-10 -10 ==
3.3 x 103.3 x 10-2 -2 ==
03/07/0103/07/01 Lecture 22Lecture 22 2525
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 == .000418.000418
7.86 x 107.86 x 108 8 == 786,000,000786,000,000
8.673 x 108.673 x 10-10 -10 == .0000000008673.0000000008673
3.3 x 103.3 x 10-2 -2 ==
03/07/0103/07/01 Lecture 22Lecture 22 2626
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 == .000418.000418
7.86 x 107.86 x 108 8 == 786,000,000786,000,000
8.673 x 108.673 x 10-10 -10 == .0000000008673.0000000008673
3.3 x 103.3 x 10-2 -2 == .033.033
03/07/0103/07/01 Lecture 22Lecture 22 2727
Scientific to Decimal Format Scientific to Decimal Format
ScientificScientific DecimalDecimal
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 == .000418.000418
7.86 x 107.86 x 108 8 == 786,000,000786,000,000
8.673 x 108.673 x 10-10 -10 == .0000000008673.0000000008673
3.3 x 103.3 x 10-2 -2 == .033.033
03/07/0103/07/01 Lecture 22Lecture 22 2828
Decimal to Scientific Format Decimal to Scientific Format
DecimalDecimal ScientificScientific
.0028.0028 ==
78,00078,000 ==
.00000167=.00000167=
.000635 =.000635 =
1,160,0001,160,000 ==
03/07/0103/07/01 Lecture 22Lecture 22 2929
Decimal to Scientific Format Decimal to Scientific Format
DecimalDecimal ScientificScientific
.0028.0028 == 2.8 x 102.8 x 10-3-3
78,00078,000 ==
.00000167=.00000167=
.000635 =.000635 =
1,160,0001,160,000 ==
03/07/0103/07/01 Lecture 22Lecture 22 3030
Decimal to Scientific Format Decimal to Scientific Format
DecimalDecimal ScientificScientific
.0028.0028 == 2.8 x 102.8 x 10-3-3
78,00078,000 == 7.8 x 107.8 x 1044
.00000167=.00000167=
.000635 =.000635 =
1,160,0001,160,000 ==
03/07/0103/07/01 Lecture 22Lecture 22 3131
Decimal to Scientific Format Decimal to Scientific Format
DecimalDecimal ScientificScientific
.0028.0028 == 2.8 x 102.8 x 10-3-3
78,00078,000 == 7.8 x 107.8 x 1044
.00000167=.00000167= 1.67 x 101.67 x 10-6-6
.000635 =.000635 =
1,160,0001,160,000 ==
03/07/0103/07/01 Lecture 22Lecture 22 3232
Decimal to Scientific Format Decimal to Scientific Format
DecimalDecimal ScientificScientific
.0028.0028 == 2.8 x 102.8 x 10-3-3
78,00078,000 == 7.8 x 107.8 x 1044
.00000167=.00000167= 1.67 x 101.67 x 10-6-6
.000635 =.000635 = 6.35 x 106.35 x 10-4-4
1,160,0001,160,000 ==
03/07/0103/07/01 Lecture 22Lecture 22 3333
Decimal to Scientific Format Decimal to Scientific Format
DecimalDecimal ScientificScientific
.0028.0028 == 2.8 x 102.8 x 10-3-3
78,00078,000 == 7.8 x 107.8 x 1044
.00000167=.00000167= 1.67 x 101.67 x 10-6-6
.000635 =.000635 = 6.35 x 106.35 x 10-4-4
1,160,0001,160,000 == 1.161.16 x 10 x 1066
03/07/0103/07/01 Lecture 22Lecture 22 3434
Changing between Scientific and Decimal FormatsChanging between Scientific and Decimal Formats
GivenGiven ChangedChanged FormatFormat
.0028.0028 ==
8200082000 ==
8.14 x 108.14 x 1033 = =
4.18 x 104.18 x 10-4 -4 ==
03/07/0103/07/01 Lecture 22Lecture 22 3535
Changing between Scientific and Decimal FormatsChanging between Scientific and Decimal Formats
GivenGiven ChangedChanged FormatFormat
.0028.0028 == 2.8 x 102.8 x 10-3-3
8200082000 ==
8.14 x 108.14 x 1033 = =
4.18 x 104.18 x 10-4 -4 ==
03/07/0103/07/01 Lecture 22Lecture 22 3636
Changing between Scientific and Decimal FormatsChanging between Scientific and Decimal Formats
GivenGiven ChangedChanged FormatFormat
.0028.0028 == 2.8 x 102.8 x 10-3-3
8200082000 == 8.2 x 108.2 x 1044
8.14 x 108.14 x 1033 = =
4.18 x 104.18 x 10-4 -4 ==
03/07/0103/07/01 Lecture 22Lecture 22 3737
Changing between Scientific and Decimal FormatsChanging between Scientific and Decimal Formats
GivenGiven ChangedChanged FormatFormat
.0028.0028 == 2.8 x 102.8 x 10-3-3
8200082000 == 8.2 x 108.2 x 1044
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 ==
03/07/0103/07/01 Lecture 22Lecture 22 3838
Changing between Scientific and Decimal FormatsChanging between Scientific and Decimal Formats
GivenGiven ChangedChanged FormatFormat
.0028.0028 == 2.8 x 102.8 x 10-3-3
8200082000 == 8.2 x 108.2 x 1044
8.14 x 108.14 x 1033 = = 8,1408,140
4.18 x 104.18 x 10-4 -4 == .000418.000418
03/07/0103/07/01 Lecture 22Lecture 22 3939
To multiply a number in scientific notation use the EE key, 5th row, 2nd column.
Use calculator to evaluate:Use calculator to evaluate:
(6.3 x 10(6.3 x 1088)(4.2 x 10)(4.2 x 1099) is ) is keyed in as keyed in as 6.36.3,, EE EE, , 88,, x x,, 4.24.2,, EE EE, , 99,, Enter Enter..
(6.3 x 10(6.3 x 1088)(4.2 x 10)(4.2 x 1099))
03/07/0103/07/01 Lecture 22Lecture 22 4040
To multiply a number in scientific notation use the EE key, 5th row, 2nd column.
Use calculator to evaluate:Use calculator to evaluate:
(6.3 x 10(6.3 x 1088)(4.2 x 10)(4.2 x 1099) is ) is keyed in as keyed in as 6.36.3,, EE EE, , 88,, x x,, 4.24.2,, EE EE, , 99,, Enter Enter..
(6.3 x 10(6.3 x 1088)(4.2 x 10)(4.2 x 1099))
The Calculator screen shows:The Calculator screen shows:6.36.3EE8 * 4.28 * 4.2EE99 2.646 x 102.646 x 101818