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Scientific Notation

MTH 4-06b. Scientific Notation. Standard form / Scientific Notation. Scientific Notation to Number Form. www.mathsrevision.com. Scientific Notation very small numbers. MTH 4-06b. Starter Questions. X. www.mathsrevision.com. Scientific Notation. MTH 4-06b. Learning Intention.

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Scientific Notation

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  1. MTH 4-06b Scientific Notation Standard form / Scientific Notation Scientific Notation to Number Form www.mathsrevision.com Scientific Notation very small numbers www.mathsrevision.com

  2. MTH 4-06b Starter Questions X www.mathsrevision.com www.mathsrevision.com

  3. Scientific Notation MTH 4-06b Learning Intention Success Criteria • To be able to use the quick method to put large numbers into scientific notation. • We are learning to write large numbers in scientific notation. www.mathsrevision.com www.mathsrevision.com

  4. Very large numbers! BOOM! MTH 4-06b How far? www.mathsrevision.com 92 000 000 miles

  5. Happy 70th Birthday! How many seconds in 70 years? Very large numbers! MTH 4-06b SPLAT! www.mathsrevision.com 70 years = 2 200 000 000 seconds!

  6. Very large numbers! MTH 4-06b Dinosaurs roamed the earth 228 million years ago www.mathsrevision.com

  7. Short hand ! MTH 4-06b = 10 1 10 = 10 2 100 = 10 x 10 = 10 3 1 000 = 10 x 10 x 10 = 10 4 10 000 = 10 x 10 x 10 x 10 www.mathsrevision.com = 10 5 100 000 = 10 x 10 x 10 x 10 x 10 = 10 6 1 000 000 = 10 x 10 x 10 x 10 x 10 x 10

  8. Standard Form MTH 4-06b = 2 x 10 2 200 = 2 x 100 = 4 x 10 3 4 000 = 4 x 1000 = 7 x 10 4 70 000 = 7 x 10 000 = 5 x 10 5 500 000 = 5 x 100 000 www.mathsrevision.com = 3 x 10 6 3 000 000 = 3 x 1 000 000 This is also known as Scientific Notation. Scale of BIG Numbers

  9. Standard Form Exercise 1 MTH 4-06b • 2 000 • (2) 20 000 • (3) 500 • (4) 800 000 • (5) 9 000 000 = 2 x 10 3 = 2 x 1000 = 2 x 10 4 = 2 x 10 000 www.mathsrevision.com = 5 x 10 2 = 5 x 100 = 8 x 10 5 = 8 x 100 000 = 9 x 10 6 = 9 x 1 000 000

  10. The point moved 6 places Add the decimal point Between 1 and 10 A short cut MTH 4-06b Move the point to get a number between 1 and 10 = 8 x 10 6 . 8 000 000 . www.mathsrevision.com

  11. The point moved 7 places Add the decimal point Between 1 and 10 A short cut MTH 4-06b Move the point to get a number between 1 and 10 = 9.2 x 10 7 . 92 000 000 . www.mathsrevision.com 9.2 x 10 7 miles

  12. The point moved 9 places Add the decimal point Between 1 and 10 A short cut MTH 4-06b Move the point to get a number between 1 and 10 = 2.2 x 10 9 . 2 200 000 000 . Happy Birthday: Seconds old! = 2.2 x 10 9

  13. The point moved 8 places Add the decimal point Between 1 and 10 A short cut MTH 4-06b Move the point to get a number between 1 and 10 = 2.28 x 10 8 228 000 000 . . www.mathsrevision.com = 2.28 x 10 8 years old

  14. Standard Form MTH 4-06b = 3 x 10 4 (1) 30 000 (2) 700 000 (3) 5 300 (4) 470 000 (5) 9 500 000 (6) 18 300 000 (7) 329 000 (8) 2 560 000 (9) 12 000 000 000 (10) 9 990 000 = 7 x 10 5 = 5.3 x 10 3 = 4.7 x 10 5 = 9.5 x 10 6 = 18.3 x 10 7 www.mathsrevision.com = 3.29 x 10 5 = 2.56 x 10 6 = 1.2 x 10 10 = 9.99 x 10 6

  15. MTH 4-06b Starter Questions www.mathsrevision.com www.mathsrevision.com

  16. MTH 4-06b Scientific Notation Learning Intention Success Criteria • Be able to expand large numbers in scientific notation to number format. • We are learning how to change large numbers from Scientific Notation to number form. www.mathsrevision.com www.mathsrevision.com

  17. The point moves 7 places Zeros after the point aren’t needed. Changing back MTH 4-06b 8.6 0000000 . =86 000 000 8.6 x 10 7 = www.mathsrevision.com Hint: Add 7 zeros, although you probably won’t need them all.

  18. The point moves 5 places Zeros after the point aren’t needed. Changing back MTH 4-06b 3.46 x 10 5 = 3.46 00000 . =346 000 www.mathsrevision.com Hint: Add 5 zeros, although you probably won’t need them all.

  19. Changing back MTH 4-06b (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 600 000 = 8 000 = 650 000 = 120 000 000 = 3 710 000 www.mathsrevision.com = 33 000 = 7 910 000 = 55 500 000 = 10 500 = 3 033 000 000

  20. Name that number! MTH 4-06b = 1 x 10 3 1 000 one thousand = 1 x 10 6 1 000 000 one million = 1 x 10 9 1 000 000 000 one billion 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 www.mathsrevision.com one googol !!! = 1 x 10 100

  21. MTH 4-06b Starter Questions www.mathsrevision.com www.mathsrevision.com

  22. MTH 4-06b Scientific Notation Learning Intention Success Criteria • Be able to change very small numbers into scientific notation and how to do the reverse process. • We are learning how to change very small numbers into Scientific Notation and vice versa. www.mathsrevision.com www.mathsrevision.com

  23. Very small numbers! MTH 4-06b www.mathsrevision.com How wide is an atom? 0.000 000 000 1 metres wide!

  24. The point moved 10 places. Negative sign for small numbers. Standard Form for small numbers MTH 4-06b Move the point to get a number between 1 and 10 = 1 x 10 -10 . 0.000 000 000 1 www.mathsrevision.com Scale of SMALL Numbers

  25. The point moved 7 places. Negative sign for small numbers. Standard Form for small numbers MTH 4-06b Move the point to get a number between 1 and 10 = 7.6 x 10 -7 . 0.000 000 76 www.mathsrevision.com

  26. The point moved 6 places. Negative sign for small numbers. Standard Form for small numbers MTH 4-06b Move the point to get a number between 1 and 10 = 1.93 x 10 -6 0.000 001 93 . www.mathsrevision.com

  27. Standard Form for small numbers MTH 4-06b (1) 0. 000 3 (2) 0.000 07 (3) 0.000 45 (4) 0.003 4 (5) 0. 000 724 (6) 0.000 000 494 (7) 0.000 095 (8) 0.000 000 098 (9) 0.000 1 03 (10) 0.000 000 000 66 www.mathsrevision.com

  28. -3 so remember to move point left for small numbers. Changing back small numbers MTH 4-06b Hint: Add 3 zeros to the left of the number. 2 x 10 -3 = 2 000 . . www.mathsrevision.com = 0.002

  29. -5 so remember to move point left for small numbers. Changing back small numbers MTH 4-06b Hint: Add 5 zeros to the left of the number. . 8.6 x 10 -5 = 8 6 00000 . www.mathsrevision.com = 0.000086

  30. -6 so remember to move point left for small numbers. Changing back small numbers MTH 4-06b Hint: Add 6 zeros to the left of the number. 5.16 x 10 -6 = . 5 16 000000 . www.mathsrevision.com = 0.000 00516

  31. Changing back small numbers MTH 4-06b (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 0.000 5 = 0.000 09 = 0.005 8 = 0.000 000 62 = 0.000 006 45 www.mathsrevision.com = 0.000 000 53 = 0.000 009 17 = 0.002 12 = 0.000 020 3 = 0.000 000 006 032

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