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UNIT: NUMBER SENSE

UNIT: NUMBER SENSE. N.S. 1.1- SCIENTIFIC NOTATION. Per 3, 5- 8/19/13 Per 2, 4, 6- 8/20/13. Note-Taking Expectations:. The title/date of each set of notes must be written on your cover sheet and your next available page in your composition book.

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UNIT: NUMBER SENSE

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  1. UNIT: NUMBER SENSE

  2. N.S. 1.1- SCIENTIFIC NOTATION Per 3, 5- 8/19/13 Per 2, 4, 6- 8/20/13

  3. Note-Taking Expectations: • The title/date of each set of notes must be written on your cover sheet and your next available page in your composition book. • You must number each page and write down which page your set of notes appear on your cover sheet. • Each set of notes must be started on a new page. • Headings must be labeled accurately (proper title, date, page number). • You must take notes on every slide UNLESS I tell you otherwise. • You may abbreviate, shorten, and paraphrase. • You must write down each step and example. • If I am going to fast, please calmly let me know and I will give you some more time. • If you see a mistake, please politely raise your hand and inform me.

  4. Each heading on my slides should be your subheading. You must underline each subheading. • If independent practice is assigned, it counts as a part of that set of notes and you can start your independent practice underneath your notes if you have space. Otherwise, you will start it on your next available page as a sub-heading.

  5. Scientific Notation: • Scientific Notation is a quick way to express very large or very small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise.

  6. Goal/Objective: You will need to be able to… • 1. Standard form into scientific notation • 2. Scientific to standard form.

  7. Form: Scientific Notation will look like this: A number × 10y Coefficient base exponent BIG NOTE: Coefficient must always be between 1 and 10.

  8. Standard Form to Scientific Notation: Example: 34,500,000,000 Step 1: Identify if starting value is less than or greater than one. greater than 1= positive exponent less than 1= negative exponent

  9. Example: 34,500,000,000 Step 2: Identify where your decimal is in the original number. Then move it to get a coefficient between 1 and 10. Step 3: Count how many places we moved the decimal to its new position. ____ places.

  10. 3.45 X _____ What is our base going to be?? What is our exponent going to be??

  11. Example 2: • Scientific Notation is also used to express very small numbers. • 0.0000567

  12. Whiteboard CFU (check for understanding) • When expressed in scientific notation, will the following number have a positive or negative exponent? • 0.000985

  13. Answer: NEGATIVE

  14. Whiteboard CFU: • When expressed in scientific notation, will the following number have a positive or negative exponent? • 42,359

  15. Answer: POSITIVE

  16. Whiteboard CFU • Express the following in scientific notation: 87,650,000,000

  17. Answer: • 8.765 x 1010

  18. Whiteboard CFU • Express the following in scientific notation: 0.000643

  19. Answer: • 6.43 x 10-4

  20. Scientific Notation to Standard Form: • Example: 5.78 x 105 Step 1: Re-write the coefficient 5.78 Step 2: Move the decimal to the right if exponent is positive. Move to the left if negative. Add zeros where necessary

  21. Check ✔ 578,000= Does our answer match the starting value? 5.78 x 105

  22. Whiteboard CFU • To express this number in standard form, do we need to move the decimal to the right or the left? 3.69 X 10-3

  23. Answer: LEFT

  24. Whiteboard CFU • To express this number in standard form, do we need to move the decimal to the right or the left? 3.57 X 105

  25. Answer: POSITIVE

  26. Whiteboard CFU • Express 4.33 x 10-6 in standard form.

  27. Answer • .00000433

  28. Whiteboard CFU • Express 2.75 x 107 in standard form.

  29. Answer: • 27,500,000

  30. Whiteboard CFU • Which of the following is NOT a correct expression of scientific notation? • a) 1.05 x 107 • b) 6.43 x 104 • c) 15.5 x 10-3 • d) 7.900 x 10-2

  31. Independent Practice NS 1.1 You must write the problem and show work. Box answer To scientific Notation: • 0.033 • 49,700 • 53,200 • 0.333 • 633,000 • 0.0572 To standard form: • 6.76 X 10-4 • 4.32 X 107 • 3.54 X 10-2 • 7.8 X 105 Answer in complete sentences. Do not write the question. • If 325,678 is converted into scientific notation, will the exponent be negative or positive? How do you know? • If .000987 is converted into scientific notation, will the exponent be negative or positive? How do you know? • If you are converting 0.327 into standard form, will you need to move the decimal to the right or to the left? How do you know?

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