1. 03/07/01Lecture 221 Unit 3 Lecture 22 Negative Exponents  Negative Exponents  Scientific Notation

2. 03/07/01Lecture 222 To evaluate exponential expressions with negative exponentsTo evaluate exponential expressions with negative exponents To write number in scientific notationTo write number in scientific notation To convert numbers in scientific notation to decimal formTo convert numbers in scientific notation to decimal form Objectives

3. 03/07/01Lecture 223 3 -4 means 1/ 3 4 b -n means 1/ b n Raising a Number to a Negative Power

4. 03/07/01Lecture 224 To raise a number to a negative power use the ^ key, and (-) key Use of the calculator to evaluate an exponential expression. 3 -4 is keyed in as 3, ^, (-), 4, ENTER.01235

5. 03/07/01Lecture 225 Use a Calculator ExpressionEvaluation 8 -2 = -6 -4 = (-6) -4 =.08 -5 =

6. 03/07/01Lecture 226 Use a Calculator ExpressionEvaluation 8 -2 =.015625 -6 -4 = (-6) -4 =.08 -5 =

7. 03/07/01Lecture 227 Use a Calculator ExpressionEvaluation 8 -2 =.015625 -6 -4 = -.000771605 (-6) -4 =.08 -5 =

8. 03/07/01Lecture 228 Use a Calculator ExpressionEvaluation 8 -2 =.015625 -6 -4 = -.000771605 (-6) -4 =.000771605.08 -5 =

9. 03/07/01Lecture 229 Use a Calculator ExpressionEvaluation 8 -2 =.015625 -6 -4 = -.000771605 (-6) -4 =.000771605.08 -5 = 305,175.7812

10. 03/07/01Lecture 2210 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 i = Interest rate per month n = Number of payments.03/12 =.0025; interest rate per month

11. 03/07/01Lecture 2211 Find the monthly payments on a 48-month car loan of $18,000 at 3% annual interest.

12. 03/07/01Lecture 2212 Find the monthly payments on a 48-month car loan of $18,000 at 3% annual interest.

13. 03/07/01Lecture 2213 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 i = Interest rate per month n = Number of payments.072/12 =.006; interest rate per month

14. 03/07/01Lecture 2214 Clintons can afford a $1000 monthly house payment at 7.2% annual interest rate for 360 months. How expensive a house can they afford?

15. 03/07/01Lecture 2215 A number in Scientific Notation has the form P x 10 n where 1<P<10 and n is an integer. 8,200,000 = Scientific Notation 8. 20 x 10 6 8. 200000. 8. 200000.

16. 03/07/01Lecture 2216 A number in Scientific Notation has the form P x 10 n where 1<P<10 and n is an integer. 8,200,000 = Scientific Notation 8. 20 x 10 6 8. 200000. 8. 200000.

17. 03/07/01Lecture 2217 A number in Scientific Notation has the form P x 10 n where 1<P<10 and n is an integer..000517 = Scientific Notation 5. 17 x 10 -4. 0005. 17

18. 03/07/01Lecture 2218 A number in Scientific Notation has the form P x 10 n where 1<P<10 and n is an integer. 7, 300, 000 Scientific Form to Decimal Form 7. 3 x 10 6 7. 300000. 7. 3 x 10 6 =

19. 03/07/01Lecture 2219 A number in Scientific Notation has the form P x 10 n where 1<P<10 and n is an integer..0003141 Scientific Form to Decimal Form 3. 141 x 10 -4. 0003. 141 3. 141 x 10 -4 =

20. 03/07/01Lecture 2220 A number in Scientific Notation has the form P x 10 n where 1<P<10 and n is an integer..000517 = Scientific Notation 5. 17 x 10 -4. 0005. 17

21. 03/07/01Lecture 2221 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 4.18 x 10 -4 = 7.86 x 10 8 = 8.673 x 10 -10 = 3.3 x 10 -2 =

22. 03/07/01Lecture 2222 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 8,140 4.18 x 10 -4 = 7.86 x 10 8 = 8.673 x 10 -10 = 3.3 x 10 -2 =

23. 03/07/01Lecture 2223 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 8,140 4.18 x 10 -4 =.000418 7.86 x 10 8 = 8.673 x 10 -10 = 3.3 x 10 -2 =

24. 03/07/01Lecture 2224 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 8,140 4.18 x 10 -4 =.000418 7.86 x 10 8 = 786,000,000 8.673 x 10 -10 = 3.3 x 10 -2 =

25. 03/07/01Lecture 2225 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 8,140 4.18 x 10 -4 =.000418 7.86 x 10 8 = 786,000,000 8.673 x 10 -10 =.0000000008673 3.3 x 10 -2 =

26. 03/07/01Lecture 2226 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 8,140 4.18 x 10 -4 =.000418 7.86 x 10 8 = 786,000,000 8.673 x 10 -10 =.0000000008673 3.3 x 10 -2 =.033

27. 03/07/01Lecture 2227 Scientific to Decimal Format ScientificDecimal 8.14 x 10 3 = 8,140 4.18 x 10 -4 =.000418 7.86 x 10 8 = 786,000,000 8.673 x 10 -10 =.0000000008673 3.3 x 10 -2 =.033

28. 03/07/01Lecture 2228 Decimal to Scientific Format DecimalScientific.0028 = 78,000 =.00000167=.000635 = 1,160,000 =

29. 03/07/01Lecture 2229 Decimal to Scientific Format DecimalScientific.0028 = 2.8 x 10 -3 78,000 =.00000167=.000635 = 1,160,000 =

30. 03/07/01Lecture 2230 Decimal to Scientific Format DecimalScientific.0028 = 2.8 x 10 -3 78,000 = 7.8 x 10 4.00000167=.000635 = 1,160,000 =

31. 03/07/01Lecture 2231 Decimal to Scientific Format DecimalScientific.0028 = 2.8 x 10 -3 78,000 = 7.8 x 10 4.00000167= 1.67 x 10 -6.000635 = 1,160,000 =

32. 03/07/01Lecture 2232 Decimal to Scientific Format DecimalScientific.0028 = 2.8 x 10 -3 78,000 = 7.8 x 10 4.00000167= 1.67 x 10 -6.000635 = 6.35 x 10 -4 1,160,000 =

33. 03/07/01Lecture 2233 Decimal to Scientific Format DecimalScientific.0028 = 2.8 x 10 -3 78,000 = 7.8 x 10 4.00000167= 1.67 x 10 -6.000635 = 6.35 x 10 -4 1,160,000 = 1.16 x 10 6

34. 03/07/01Lecture 2234 Changing between Scientific and Decimal Formats Given Changed Format.0028 = 82000 = 8.14 x 10 3 = 4.18 x 10 -4 =

35. 03/07/01Lecture 2235 Changing between Scientific and Decimal Formats Given Changed Format.0028 = 2.8 x 10 -3 82000 = 8.14 x 10 3 = 4.18 x 10 -4 =

36. 03/07/01Lecture 2236 Changing between Scientific and Decimal Formats Given Changed Format.0028 = 2.8 x 10 -3 82000 = 8.2 x 10 4 8.14 x 10 3 = 4.18 x 10 -4 =

37. 03/07/01Lecture 2237 Changing between Scientific and Decimal Formats Given Changed Format.0028 = 2.8 x 10 -3 82000 = 8.2 x 10 4 8.14 x 10 3 = 8,140 4.18 x 10 -4 =

38. 03/07/01Lecture 2238 Changing between Scientific and Decimal Formats Given Changed Format.0028 = 2.8 x 10 -3 82000 = 8.2 x 10 4 8.14 x 10 3 = 8,140 4.18 x 10 -4 =.000418

39. 03/07/01Lecture 2239 To multiply a number in scientific notation use the EE key, 5 th row, 2 nd column. Use calculator to evaluate: (6.3 x 10 8 )(4.2 x 10 9 ) is keyed in as 6.3, EE, 8, x, 4.2, EE, 9, Enter. (6.3 x 10 8 )(4.2 x 10 9 )

40. 03/07/01Lecture 2240 To multiply a number in scientific notation use the EE key, 5 th row, 2 nd column. Use calculator to evaluate: (6.3 x 10 8 )(4.2 x 10 9 ) is keyed in as 6.3, EE, 8, x, 4.2, EE, 9, Enter. (6.3 x 10 8 )(4.2 x 10 9 ) The Calculator screen shows: 6.3 E 8 * 4.2 E 9 2.646 x 10 18 2.646 x 10 18