Скачать презентацию Unit 3 Lecture 22 Negative Exponents 4 Scientific Скачать презентацию Unit 3 Lecture 22 Negative Exponents 4 Scientific

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Unit 3 Lecture 22 Negative Exponents 4 Scientific Notation 03/07/01 Lecture 22 1 Unit 3 Lecture 22 Negative Exponents 4 Scientific Notation 03/07/01 Lecture 22 1

Objectives • To evaluate exponential expressions with negative exponents • To write number in Objectives • To evaluate exponential expressions with negative exponents • To write number in scientific notation • To convert numbers in scientific notation to decimal form 03/07/01 Lecture 22 2

Raising a Number to a Negative Power -n means 1/ b n b -4 Raising a Number to a Negative Power -n means 1/ b n b -4 means 1/ 34 3 03/07/01 Lecture 22 3

Use of the calculator to evaluate an exponential expression. To raise a number to Use of the calculator to evaluate an exponential expression. To raise a number to a negative power use the ^ key, and (-) key 3 -4 is keyed in as 3, ^, (-), 4, ENTER 03/07/01 . 01235 Lecture 22 4

Use a Calculator Expression Evaluation 8 -2 = -6 -4 = (-6)-4 =. 08 Use a Calculator Expression Evaluation 8 -2 = -6 -4 = (-6)-4 =. 08 -5 = 03/07/01 Lecture 22 5

Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = (-6)-4 Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = (-6)-4 =. 08 -5 = 03/07/01 Lecture 22 6

Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = -. Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = -. 000771605 (-6)-4 =. 08 -5 = 03/07/01 Lecture 22 7

Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = -. Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = -. 000771605 (-6)-4 = . 000771605 . 08 -5 = 03/07/01 Lecture 22 8

Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = -. Use a Calculator Expression Evaluation 8 -2 = . 015625 -6 -4 = -. 000771605 (-6)-4 = . 000771605 . 08 -5 = 305, 175. 7812 03/07/01 Lecture 22 9

Find the monthly payments on a 48 -month car loan of $18, 000 at Find the monthly payments on a 48 -month car loan of $18, 000 at 3% annual interest. P = Monthly payment A = Amount of loan i = Interest rate per month n = Number of payments. 03/12 =. 0025; interest rate per month 03/07/01 Lecture 22 10

Find the monthly payments on a 48 -month car loan of $18, 000 at Find the monthly payments on a 48 -month car loan of $18, 000 at 3% annual interest. 03/07/01 Lecture 22 11

Find the monthly payments on a 48 -month car loan of $18, 000 at Find the monthly payments on a 48 -month car loan of $18, 000 at 3% annual interest. 03/07/01 Lecture 22 12

Clintons can afford a $1000 monthly house payment at 7. 2% annual interest rate Clintons can afford a $1000 monthly house payment at 7. 2% annual interest rate for 360 months. How expensive a house can they afford? P = Monthly payment A = Amount of loan i = Interest rate per month n = Number of payments . 072/12 =. 006; interest rate per month 03/07/01 Lecture 22 13

Clintons can afford a $1000 monthly house payment at 7. 2% annual interest rate Clintons can afford a $1000 monthly house payment at 7. 2% annual interest rate for 360 months. How expensive a house can they afford? 03/07/01 Lecture 22 14

Scientific Notation A number in Scientific Notation has the form P x 10 n Scientific Notation A number in Scientific Notation has the form P x 10 n where 1

Scientific Notation A number in Scientific Notation has the form P x 10 n Scientific Notation A number in Scientific Notation has the form P x 10 n where 1

Scientific Notation A number in Scientific Notation has the form P x 10 n Scientific Notation A number in Scientific Notation has the form P x 10 n where 1

Scientific Form to Decimal Form A number in Scientific Notation has the form P Scientific Form to Decimal Form A number in Scientific Notation has the form P x 10 n where 1

Scientific Form to Decimal Form A number in Scientific Notation has the form P Scientific Form to Decimal Form A number in Scientific Notation has the form P x 10 n where 1

Scientific Notation A number in Scientific Notation has the form P x 10 n Scientific Notation A number in Scientific Notation has the form P x 10 n where 1

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 4. 18 x Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 4. 18 x 10 -4 = 7. 86 x 108 = 8. 673 x 10 -10 = 3. 3 x 10 -2 = 03/07/01 Lecture 22 21

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = 7. 86 x 108 = 8. 673 x 10 -10 = 3. 3 x 10 -2 = 03/07/01 Lecture 22 22

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = . 000418 7. 86 x 108 = 8. 673 x 10 -10 = 3. 3 x 10 -2 = 03/07/01 Lecture 22 23

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = . 000418 7. 86 x 108 = 786, 000 8. 673 x 10 -10 = 3. 3 x 10 -2 = 03/07/01 Lecture 22 24

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = . 000418 7. 86 x 108 = 786, 000 8. 673 x 10 -10 =. 000008673 3. 3 x 10 -2 = 03/07/01 Lecture 22 25

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = . 000418 7. 86 x 108 = 786, 000 8. 673 x 10 -10 =. 000008673 3. 3 x 10 -2 = 03/07/01 Lecture 22 . 033 26

Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. Scientific to Decimal Format Scientific Decimal 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = . 000418 7. 86 x 108 = 786, 000 8. 673 x 10 -10 =. 000008673 3. 3 x 10 -2 = 03/07/01 Lecture 22 . 033 27

Decimal to Scientific Format Decimal Scientific . 0028 = 78, 000 =. 00000167=. 000635 Decimal to Scientific Format Decimal Scientific . 0028 = 78, 000 =. 00000167=. 000635 = 1, 160, 000 = 03/07/01 Lecture 22 28

Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 78, 000 =. 00000167=. 000635 = 1, 160, 000 = 03/07/01 Lecture 22 29

Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 78, 000 = 7. 8 x 104 . 00000167=. 000635 = 1, 160, 000 = 03/07/01 Lecture 22 30

Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 78, 000 = 7. 8 x 104 . 00000167= 1. 67 x 10 -6 . 000635 = 1, 160, 000 = 03/07/01 Lecture 22 31

Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 Decimal to Scientific Format Decimal Scientific . 0028 = 2. 8 x 10 -3 78, 000 = 7. 8 x 104 . 00000167= 1. 67 x 10 -6 . 000635 = 6. 35 x 10 -4 1, 160, 000 = 03/07/01 Lecture 22 32

Decimal to Scientific Format Decimal Scientific . 0028 = 78, 000 = 7. 8 Decimal to Scientific Format Decimal Scientific . 0028 = 78, 000 = 7. 8 x 104 . 00000167= 1. 67 x 10 -6 . 000635 = 6. 35 x 10 -4 1, 160, 000 = 03/07/01 2. 8 x 10 -3 1. 16 x 106 Lecture 22 33

Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 82000 = Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 82000 = 8. 14 x 103 = 4. 18 x 10 -4 = 03/07/01 Lecture 22 34

Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 2. 8 Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 2. 8 x 10 -3 82000 = 8. 14 x 103 = 4. 18 x 10 -4 = 03/07/01 Lecture 22 35

Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 2. 8 Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 2. 8 x 10 -3 82000 = 8. 2 x 104 8. 14 x 103 = 4. 18 x 10 -4 = 03/07/01 Lecture 22 36

Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 2. 8 Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 2. 8 x 10 -3 82000 = 8. 2 x 104 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = 03/07/01 Lecture 22 37

Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 82000 = Changing between Scientific and Decimal Formats Given Changed Format . 0028 = 82000 = 8. 2 x 104 8. 14 x 103 = 8, 140 4. 18 x 10 -4 = 03/07/01 2. 8 x 10 -3 . 000418 Lecture 22 38

Use calculator to evaluate: (6. 3 x 108)(4. 2 x 109) To multiply a Use calculator to evaluate: (6. 3 x 108)(4. 2 x 109) To multiply a number in scientific notation use the EE key, 5 th row, 2 nd column. (6. 3 x 108)(4. 2 x 109) is keyed in as 6. 3, EE, 8, x, 4. 2, EE, 9, Enter. 03/07/01 Lecture 22 39

Use calculator to evaluate: (6. 3 x 108)(4. 2 x 109) To multiply a Use calculator to evaluate: (6. 3 x 108)(4. 2 x 109) To multiply a number in scientific notation use the EE key, 5 th row, 2 nd column. (6. 3 x 108)(4. 2 x 109) is keyed in as 6. 3, EE, 8, x, 4. 2, EE, 9, Enter. The Calculator screen shows: 6. 3 E 8 * 4. 2 E 9 03/07/01 2. 646 x 1018 Lecture 22 40