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. Actual number Rounded to the nearest Correct choice Number of sig. fig. 152 508100 000200 0001 152 50810 000 152 5081 000 152 508100 152 50810

7. Complete the table. Actual number Rounded to the nearest Correct choice Number of sig. fig. 152 508100 000200 0001 152 50810 000150 0002 152 5081 000153 0003 152 508100152 5004 152 50810152 5105

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. ServiceFee ($)Rounded to nearest Rounded fee Sig. Fig. Electrician 1299.89 $14 Surgeon1303 $10 Solicitor1297 $100

15. Complete the table. ServiceFee ($)Rounded to nearest Rounded fee Sig. Fig. Electrician 1299.89 $1$13004 Surgeon1303 $10$13003 Solicitor1297 $100$13002

16. Standard Notation (Scientific Form) 10 000 000 000 000. This number does not fit into most calculators. The number can be written as 10 13 or 1 x 10 13.

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. 10 13 When 1 kg of mass is completely converted to energy it produces about 100 000 000 000 000 joules of energy. 10 14 The number of atoms in your body is about 1 000 000 000 000 000 000 000 000 000. 10 27

19. Write the following in decimal form. 3.6 x 10 = 3.6 x 10 2 = 3.6 x 10 3 = 4.3 x 10 5 = 1.03 x 10 7 =

20. Write the following in decimal form. 3.6 x 10 = 36 3.6 x 10 2 = 360 3.6 x 10 3 = 3600 4.3 x 10 5 = 430 000 1.03 x 10 7 = 1 030 000

21. Standard form 9.63 x 10 4 is in standard form. 96.3 x 10 3 is not in standard form.

22. Which of the following are in standard form? 9.8 x 10 3 98 x 10 2 980 x 10 1 3.4 x 10 5 0.34 x 10 6 0.034 x 10 7 11.8 x 10 8

23. Which of the following are in standard form? 9.8 x 10 3 Yes 98 x 10 2 No 980 x 10 1 No 3.4 x 10 5 Yes 0.34 x 10 6 No 0.034 x 10 7 No 11.8 x 10 8 No

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 10 8 The volume of the earth ≈ 1 080 000 000 000 cubic kilometres. 1.08 x 10 12 The length of the equator ≈ 40 020 km. 4.002 x 10 4 The distance sound travels in one minute ≈ 19 700 m. 1.97 x 10 4

26. Complete the table. (Sig. fig. are underlined) AmountRounded to nearest Number sig. fig. Standard form 400.00Cent54.0000 x 10 2 400.00 4.00 x 10 2 400.00 4 x 10 2

27. Complete the table. (Sig. fig. are underlined) AmountRounded to nearest Number sig. fig. Standard form 400.00Cent54.0000 x 10 2 400.0010 c44.000 x 10 2 400.00$134.00 x 10 2 400.00$1024.0 x 10 2 400.00$10014 x 10 2

28. Light from the Great Galaxy in Andromeda takes about 2.3 x 10 6 years to reach Earth. Light travels at about 2.998 x 10 5 km/s. How many sig. fig. in 2.3 x 10 6 ? How many sig. fig. in 2.998 x 10 5 ? How many seconds are there in 2.3 x 10 6 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 10 6 years to reach Earth. Light travels at about 2.998 x 10 5 km/s. How many sig. fig. in 2.3 x 10 6 ? 2 How many sig. fig. in 2.998 x 10 5 ? 4 How many seconds are there in 2.3 x 10 6 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 10 6 x 365.25 x 24 x 60 x 60 x 2.998 x 10 5 = 2.2 x 10 19 km

30. The speed of light is about 2.998 x 10 5 km/s. Light from the Sun takes 5.00 x 10 2 seconds to reach Earth. How far is the Earth from the Sun? (Round sensibly.)

31. The speed of light is about 2.998 x 10 5 km/s. Light from the Sun takes 5.00 x 10 2 seconds to reach Earth. How far is the Earth from the Sun? (Round sensibly) 2.998 x 10 5 x 5.00 x 10 2 = 1.50 x 10 8 km Rounded to 3 sig. fig.

32. The surface area of a sphere of radius r is about (1.2566 x 10 1 ) x r 2. The radius of the earth is about 6.37 x 10 6 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 10 1 ) x r 2. The radius of the earth is about 6.37 x 10 6 metres. Find the surface area of the earth in A.square metres 5.64 x 10 14 B.square kilometres 5.64 x 10 8

34. Write in power form 0.010.000 01 0.0010.1 0.000 000 000 1 0.000 000 000 01

35. Write in power form 0.0110 -2 0.000 0110 -5 0.00110 -3 0.110 -1 0.000 000 000 1 10 -10 0.000 000 000 01 10 -11

36. Complete the table 2 2 -2 2121 2 -1 2020 2 -3

37. Complete the table 2 42 -2 1/4 2121 22 -1 1/2 2020 12 -3 1/8

38. Complete the table 3232 3 -2 3131 3 -1 3030 3 -3

39. Complete the table 3232 93 -2 1/9 3131 33 -1 1/3 3030 13 -3

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

41. Write the following in standard form 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

42. A proton is moving at 2.8 x 10 8 m/s in a cyclotron. How far will the proton travel in 3.2 x 10 -5 seconds?

43. A proton is moving at 2.8 x 10 8 m/s in a cyclotron. How far will the proton travel in 3.2 x 10 -5 seconds? 8960 m = 9.0 x 10 3 m (2 sig. fig.)

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

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

46. Complete this estimate. 10 11

47. Estimate and then work out the following.