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Standard Form. Number Sense. “135 000 will get family care soon”. The actual number of families granted family care is 135 148. This number has been rounded by the reporter to 135 000. How many significant figures are there in the rounded number?. “135 000 will get family care soon”.

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Standard Form

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  1. Standard Form Number Sense

  2. “135 000 will get family care soon” • The actual number of families granted family care is 135 148. • This number has been rounded by the reporter to 135 000. • How many significant figures are there in the rounded number?

  3. “135 000 will get family care soon” • The actual number of families granted family care is 135 148. • This number has been rounded by the reporter to 135 000. • How many significant figures are there in the rounded number? • 3 as the number is rounded to the nearest thousand.

  4. “145 000 applications have been processed.” • What is the lowest number of applications that this number represents? • What is the highest number of applications that this number represents?

  5. “145 000 applications have been processed.” • What is the lowest number of applications that this number represents? 144 500 • What is the highest number of applications that this number represents? 145 499

  6. Complete the table.

  7. Complete the table.

  8. A sack of coal weighs 50 kg to the nearest kilogram. • What weights would be acceptable for the following? • The least weight. • The greatest weight.

  9. A sack of coal weighs 50 kg to the nearest kilogram. • What weights would be acceptable for the following? • The least weight. 49.5 kg • The greatest weight. 50.4999… kg

  10. A sack of coal weighs 50 kg to the nearest kilogram. • Which of these weights represents a short weighing? • 49.6 kg • 49.4 kg • 49.49 kg • 49.5 kg

  11. A sack of coal weighs 50 kg to the nearest kilogram. • Which of these weights represents a short weighing? • 49.6 kg • 49.4 kg - will round to 49 kg • 49.49 kg - will round to 49 kg • 49.5 kg

  12. An AA sign tells motorists that Hamilton is 56 km away. • Where in Hamilton is the distance 56 km measured to? • A motorist checks her odometer and notes the distance to be 55.8 km. Who is correct, the motorist or the AA?

  13. An AA sign tells motorists that Hamilton is 56 km away. • Where in Hamilton is the distance 56 km measured to? The central post office. • A motorist checks her odometer and notes the distance to be 55.8 km. Who is correct, the motorist or the AA? • Both are correct. The AA has rounded the distance to the nearest whole number.

  14. Complete the table.

  15. Complete the table.

  16. Standard Notation(Scientific Form) • 10 000 000 000 000. • This number does not fit into most calculators. • The number can be written as 1013 or • 1 x 1013.

  17. Write the following numbers in power form. • The distance to the nearest star is about 10 000 000 000 000 km. • When 1 kg of mass is completely converted to energy it produces about 100 000 000 000 000 joules of energy. • The number of atoms in your body is about 1 000 000 000 000 000 000 000 000 000.

  18. Write the following numbers in power form. • The distance to the nearest star is about 10 000 000 000 000 km. 1013 • When 1 kg of mass is completely converted to energy it produces about 100 000 000 000 000 joules of energy. 1014 • The number of atoms in your body is about 1 000 000 000 000 000 000 000 000 000. 1027

  19. Write the following in decimal form. • 3.6 x 10 = • 3.6 x 102 = • 3.6 x 103 = • 4.3 x 105 = • 1.03 x 107 =

  20. Write the following in decimal form. • 3.6 x 10 = 36 • 3.6 x 102 = 360 • 3.6 x 103 = 3600 • 4.3 x 105 = 430 000 • 1.03 x 107 = 1 030 000

  21. Standard form • 9.63 x 104 is in standard form. • 96.3 x 103 is not in standard form.

  22. Which of the following are in standard form? • 9.8 x 103 • 98 x 102 • 980 x 101 • 3.4 x 105 • 0.34 x 106 • 0.034 x 107 • 11.8 x 108

  23. Which of the following are in standard form? • 9.8 x 103Yes • 98 x 102 No • 980 x 101 No • 3.4 x 105Yes • 0.34 x 106 No • 0.034 x 107No • 11.8 x 108No

  24. Write the following in scientific notation (standard form) • The speed of light ≈ 300 000 000 m/s • The volume of the earth ≈ 1 080 000 000 000 cubic kilometres. • The length of the equator ≈ 40 020 km. • The distance sound travels in one minute ≈ 19 700 m.

  25. Write the following in scientific notation (standard form) • The speed of light ≈ 300 000 000 m/s • 3 x 108 • The volume of the earth ≈ 1 080 000 000 000 cubic kilometres. 1.08 x 1012 • The length of the equator ≈ 40 020 km. • 4.002 x 104 • The distance sound travels in one minute ≈ 19 700 m. 1.97 x 104

  26. Complete the table. (Sig. fig. are underlined)

  27. Complete the table. (Sig. fig. are underlined)

  28. Light from the Great Galaxy in Andromeda takes about 2.3 x 106 years to reach Earth.Light travels at about 2.998 x 105 km/s. • How many sig. fig. in 2.3 x 106? • How many sig. fig. in 2.998 x 105? • How many seconds are there in 2.3 x 106 years? • Round your answer to 2 sig. fig. • Distance = speed x time. What is the distance from Earth to the Great Galaxy in Andromeda?

  29. Light from the Great Galaxy in Andromeda takes about 2.3 x 106 years to reach Earth.Light travels at about 2.998 x 105 km/s. • How many sig. fig. in 2.3 x 106?2 • How many sig. fig. in 2.998 x 105? 4 • How many seconds are there in 2.3 x 106 years? 2 • Round your answer to 2 sig. fig. • Distance = speed x time. What is the distance from Earth to the Great Galaxy in Andromeda?2.3 x 106 x 365.25 x 24 x 60 x 60 x 2.998 x 105 = 2.2 x 1019 km

  30. The speed of light is about 2.998 x 105 km/s. • Light from the Sun takes 5.00 x 102 seconds to reach Earth. How far is the Earth from the Sun? (Round sensibly.)

  31. The speed of light is about 2.998 x 105 km/s. • Light from the Sun takes 5.00 x 102 seconds to reach Earth. How far is the Earth from the Sun? (Round sensibly) 2.998 x 105 x 5.00 x 102 = 1.50 x 108 km Rounded to 3 sig. fig.

  32. The surface area of a sphere of radius r is about (1.2566 x 101) x r2. The radius of the earth is about 6.37 x 106 metres. • Find the surface area of the earth in • A. square metres • B. square kilometres

  33. The surface area of a sphere of radius r is about (1.2566 x 101) x r2. The radius of the earth is about 6.37 x 106 metres. • Find the surface area of the earth in • A. square metres 5.64 x 1014 • B. square kilometres 5.64 x 108

  34. Write in power form

  35. Write in power form

  36. Complete the table

  37. Complete the table

  38. Complete the table

  39. Complete the table

  40. 5-2 2-5 5-3 10-3 6-1 Write the following as fractions.

  41. 0.071 0.0073 19.04 0.0000346 0.02003 7.1 x 10-2 7.3 x 10-3 1.904 x 10-1 3.46 x 10-5 2.003 x 10-2 Write the following in standard form

  42. How far will the proton travel in 3.2 x 10-5 seconds? A proton is moving at 2.8 x 108 m/s in a cyclotron.

  43. How far will the proton travel in 3.2 x 10-5 seconds? 8960 m = 9.0 x 103 m (2 sig. fig.) A proton is moving at 2.8 x 108 m/s in a cyclotron.

  44. What is its speed (to 2 sig. fig.)? Another proton moves 2.3 x 10-1 m in 9.7 x 10-5 s.

  45. What is its speed (to 2 sig. fig.)? 2371 m/s = 2.4 x 102 m/s Another proton moves 2.3 x 10-1 m in 9.7 x 10-5 s.

  46. Complete this estimate. • 1011

  47. Estimate and then work out the following.

  48. Estimate and then work out the following.

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