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