1 / 27

Section 8.3: Scientific Notation

Section 8.3: Scientific Notation. Objective The student will be able to: Express numbers in scientific and decimal notation. How wide is our universe?. 210,000,000,000,000,000,000,000 miles (22 zeros)

joseph-carroll
Download Presentation

Section 8.3: Scientific Notation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 8.3: Scientific Notation ObjectiveThe student will be able to: • Express numbers in scientific and decimal notation

  2. How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

  3. Who uses this? • Astronomers often work with very large numbers such as the masses of planets. The mass of each planet in the solar system is given on the next slide. Notice each value is written as the product of a number and a power of 10. These values are written in scientific notation.

  4. Scientific Notation in Astronomy Mercury 3.30x10^23 Venus 4.87x10^24 Earth 5.97x10^24 Mars 6.42X10^23 Jupiter 1.90x10^27 Saturn 5.69x10^26 Uranus 8.68x10^25 Neptune 1.02x10^26 Pluto 1.27x10^22

  5. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer

  6. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

  7. 2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

  8. Positive Exponents (large #’s) Example 1: 2.45 x 108 Example 2: 2.19 x 105 Example 3: 30,500,000 Example 4: 3,022,000,000,000

  9. Ex. 5) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

  10. Negative Exponents (small #’s) • Example 6: 3 x 10-5 • Example 7: 7.48 x 10-3 • Example 8: 0.000000672 • Example 9: 0.000781

  11. 10) You Try: Write 28750.9 in scientific notation. A. 2.87509 x 10-5 B. 2.87509 x 10-4 C. 2.87509 x 104 D. 2.87509 x 105

  12. You Try a few… A) 2 x 10-8 B) 4.59 x 103 C) 7.183 x 1014 D) 3.6 x 10-5 E) 56,700,000 F) 0.00567 G) 0.00000000004

  13. Review Positive Exponents = LARGE numbers • Move the decimals to the RIGHT Negative Exponents = SMALL numbers • Move the decimals to the LEFT

  14. 11) Express 1.8 x 10-4 in decimal notation. 0.00018 12) Express 4.58 x 106 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button. 4.58 x 106 is typed 4.58 6

  15. You Try: • Find YOUR textbook and complete the following: page 402 #16-44 Odd, 46-53 • Turn in for a CW grade. Please ask the neighbor for assistance.

  16. Warm-Up, Write the following in scientific notation 1. 984000000 2. 0.00058 3. 560 x 10 3

  17. Answer Key • 1. 9.84 x 108 • 2. 5.8 x 10-4 • 3. 5.6 x 105

  18. There is more to sci. notation • Numbers in scientific notation can be multiplied or divided. First multiply the decimals, then apply the product of powers or quotient of powers property to simplify the powers of 10. Next, rewrite the decimal in scientific notation and simplify the powers.. Let’ see….

  19. Example 1: Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2 You must include parentheses (4.5 x 10 -5) (1.6 x 10 -2) 0.0028125 Write in scientific notation. 2.8125 x 10-3

  20. Ex. 2: Use a calculator to evaluate: 7.2 x 10-9 1.2 x 102On the calculator, the answer is: 6.E -11, E = exponent!!! The answer in scientific notation is 6 x 10 -11 The answer in decimal notation is 0.00000000006

  21. Ex. 3: Use a calculator to evaluate (0.0042)(330,000).On the calculator, the answer is 1386. The answer in decimal notation is 1386 The answer in scientific notation is 1.386 x 103

  22. Ex. 4: Use a calculator to evaluate (3,600,000,000)(23).On the calculator, the answer is: 8.28 E +10, E = exponent The answer in scientific notation is 8.28 x 10 10 The answer in decimal notation is 82,800,000,000

  23. Ex. 5: Write (2.8 x 103)(5.1 x 10-7) in scientific notation. A. 14.28 x 10-4 B. 1.428 x 10-3 C. 14.28 x 1010 D. 1.428 x 1011

  24. You Try, write in scientific and standard notation • (5.3 x 102)(4.1 x 105) • (2 x 10-5)(9.4 x 10-3) • 1.5 x 1022.5 x 1012 • 1.25 x 1042.5 x 10-6

  25. You practice • Find your textbook and practice page 429 #44-55. Turn in for a CW grade. • I should hear you talking and communicating with each other!

  26. Write in PROPER scientific notation.(Notice the number is not between 1 and 10) Example 6) 234.6 x 109 2.346 x 1011 Example 7) 0.0642 x 104 on calculator: 642 6.42 x 10 2

  27. Ex. 9: Write 531.42 x 105 in scientific notation. • .53142 x 102 • 5.3142 x 103 • 53.142 x 104 • 531.42 x 105 • 53.142 x 106 • 5.3142 x 107 • .53142 x 108

More Related