1 / 32

Scientific Notation

Scientific Notation. What is Scientific Notation?. Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise. Why use scientific notation?.

keegan
Download Presentation

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. Scientific Notation

  2. What is Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise.

  3. Why use scientific notation? • For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. • Numbers expressed in scientific notation makes it easier to solve problems with big and small numbers.

  4. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x Are the following in scientific notation?

  5. Changing standard form to scientific notation.

  6. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

  7. Continued… • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

  8. When changing from Standard Notation to Scientific Notation: See if the original number is greater than or less than one. • If the number is greater than one, the exponent will bepositive. 348943 = 3.489 x 105 • If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8

  9. When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10-7

  10. The Distance From the Sun to the Earth 93,000,000

  11. Step 1 • Move decimal left • Leave only one number in front of decimal 93,000,000 = 9.3000000

  12. Step 2 • Write number without zeros 93,000,000 = 9.3

  13. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  14. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

  15. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

  16. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

  17. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 • 7.34 x 108 2)8.7 x 1011

  18. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

  19. Example 1 • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer: 2.898 x 108

  20. Example 2 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4

  21. Try Build a Bridge #1 #2

  22. Try changing these numbers from Standard Notation to Scientific Notation: 9.872432 x 106 • 9872432 • .0000345 • .08376 • 5673 3.45 x 10-5 8.376 x 102 5.673 x 103

  23. Changing scientific notation to standard form.

  24. To change scientific notation to standard form… • Move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

  25. An easy way to remember this is: • If an exponent is positive, the number gets larger, so move the decimal to the right. • If an exponent is negative, the number gets smaller, so move the decimal to the left.

  26. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

  27. Example • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right)

  28. Example • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

  29. Write in Standard Form • 6.27 x 106 • 9.01 x 104 • 6,270,000 • 90,100 Move the decimal to the right.

  30. Try changing these numbers from Scientific Notation to Standard Notation: 96780 • 9.678 x 104 • 7.4521 x 10-3 • 8.513904567 x 107 • 4.09748 x 10-5 .0074521 85139045.67 .0000409748

  31. Try Build a Bridge #3 #4

  32. Guided PracticeHomework: Practice

More Related