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Measurement

Measurement. Chapter 2. International System (SI) units. International System (SI) units. Examples:. Density is defined as mass per unit volume. Write the SI unit for density. Mass: kg Volume: Density:

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Measurement

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  1. Measurement Chapter 2

  2. International System (SI) units

  3. International System (SI) units

  4. Examples: • Density is defined as mass per unit volume. Write the SI unit for density. Mass: kg Volume: Density: • A newton is defined as the force which accelerates a mass of 1 kg at the rate of . Write down the combinations of SI units which define a newton. 1 kilogram x 1 m per second per second

  5. Examples: c) Convert 3540 millimetres into metres. milli means d) 7.14 kilograms into grams. e) 4 hrs and 12 min into seconds. f) 15 knots into km/h

  6. Complete • Exercise 2A page 30 • Questions 1 – 10

  7. Scientific Notation (Standard Form) • Writing numbers as a number between 1 and 10, multiplied by a power of 10. • Using the calculator: press EXP instead of • Type 5.38 EXP 9, then EXE

  8. Examples: Write in scientific notation a) 944800000 =9.448 x 108 b) 0.0000616 =6.16 x 10-5

  9. Examples: Write as a decimal number a) 4.201 x 104 = 42010 b) 3.7041 x 10-8 =0.000000037041

  10. Examples: Using the calculator a) 870000 x 95000000 = 82650000000000 b) = 0.000000000775

  11. Complete • Exercise 2B page 33 • Q1, • Q3: a, c, e, g, • Q4: a, c, e, g, • Q5: a ,c e, g, • Q6: a, c, e, g, • Q7: a, c, e, h, • Q11

  12. Rounding Whole Numbers • If the digit after the one being rounded is a 0, 1, 2, 3, 4 we round down. • If the digit after the one being rounded is a 5, 6, 7, 8, 9 we round up.

  13. Examples: Round to the nearest 10 • 48 • 583 • 5705

  14. Examples: Rounding to the nearest 100 • 452 • 37239

  15. Complete: Exercise 2C.1 page 34 • Q1: a, c, e, g, i, k • Q2: a, c, e, g • Q3: a, c, e, g • Q4: a, c, e, g

  16. Round Decimal Numbers • If the digit after the one being rounded is a 0, 1, 2, 3, 4 we round down. • If the digit after the one being rounded is a 5, 6, 7, 8, 9 we round up.

  17. Examples: Round to the number of decimal places in the brackets • 3.27 (1) • 6.3829 (2) • (2.8 + 3.7)(0.82 – 0.57) (2) =1.625 • 18.6 - (2) =17.08076923

  18. Complete: Exercise 2C.2 page 36 • Q1: a, c, e, g, i • Q2: a, c, e, g, i • Q3

  19. Rounding off to significant figures • To round off to n significant figures we look at the (n + 1)th digit. • 0, 1, 2, 3, 4 we do not change the nth digit • 5, 6, 7, 8, 9 we increase the nth digit by 1 • We delete all digits after the nth digit, replacing by 0’s if necessary.

  20. Examples: • 7.182 to 2 significant figures • 0.00132 to 2 significant figures • 423 to 1 significant figure • 4.057 to 3 significant figures

  21. Complete: Exercise 2C.3 page 37 • Q1: b, d, f, h, j • Q2: b, d, f, h, j • Q3: b, d, f, h, j • Q4 • Q5: a, c, e • Q7: a, c, e • Q8: a, b, c

  22. Approximation and estimation

  23. Accuracy of measurements

  24. Complete: Exercise 2D.1 page 42 • Q2, 3, 4, 6, 7, 8, 9

  25. Absolute and Percentage error • Error: the difference between our measurement and the actual measurement. • Absolute error: the size or the magnitude of the error. Absolute error = approximate value – exact value Percentage error =

  26. Example 1: You estimate a fences length to be 70m where as it’s true length is 78.3m. Find correct to one decimal place the: a) Absolute error: • Percentage error:

  27. Example 2: Alan wants to lay carpet on his 4.2 m x 5.1 m lounge floor. He estimates the area by rounding each of the measurements to the nearest metre. d) Find the percentage error. e) Will Alan have enough carpet to cover his lounge room. How should he have rounded the measurements? No he will be 1.42m2 short. He should have rounded up his measurements • Find Alan’s estimate of the lounge. b) The carpet costs $39 per square metre. Find the cost of the carpet using Alan’s estimate. c) Find the actual area.

  28. Complete: Exercise 2D.2 page 44 • Q1: a, c • Q2: a, c • Q3 • Q5

  29. Rates: Speed A rate is an ordered comparison of quantities of different kinds

  30. Example 1: A car is travelling a distance of 325km. • Find the average speed if the time taken is 4 h 17 min. b) The time taken if the average speed is .

  31. Complete: Exercise 2E.1 page 47 • Q1a, c, 2, 3, 4, 5, 6

  32. Rates: Flow

  33. Example: Amber is filling a bucket from a tap. The bucket holds 12L, and it takes 30 seconds to fill. Write the rate of flow from the tap in: a) b)

  34. Complete: Exercise 2E.2 page 48 Q1, 2, 3

  35. Rates: Density

  36. Example: The density of Aluminium is . Find the mass of an Aluminium bar which is 2.4 m by 10 cm by 5cm. 2.4 m = 240 cm Volume:

  37. Complete: Exercise 2E.3 page 49 Q1-4

  38. Other rate problems Example: Convert the price of 35 apples bought for $9.45 to a rate of cents per apple.

  39. Complete: Exercise 2E.4 page 49 • Q1: a, c, e, g • Q2, 3, 6, 8

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