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Approximation

Approximation. Objectives for today’s lesson : Practice Upper & Lower Bounds Using Rounding appropriately Finding bounds on answers. Starter. In pairs, try and find pairs of numbers which are the same when rounded to : 1 decimal place and 2 significant figures 3 dp’s and 7 sf’s.

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Approximation

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  1. Approximation Objectives for today’s lesson : • Practice Upper & Lower Bounds • Using Rounding appropriately • Finding bounds on answers

  2. Starter In pairs, try and find pairs of numbers which are the same when rounded to : • 1 decimal place and 2 significant figures • 3 dp’s and 7 sf’s

  3. Upper & Lower bounds Find the upper & lower bounds of these numbers which are rounded to 2 significant figures : LowerUpper 38 37.5 38.5 99 140 10 1100 0.035

  4. Upper & Lower bounds Find the upper & lower bounds of these numbers which are rounded to 2 significant figures : LowerUpper 38 37.5 38.5 99 98.5 99.5 140 10 1100 0.035

  5. Upper & Lower bounds Find the upper & lower bounds of these numbers which are rounded to 2 significant figures : LowerUpper 38 37.5 38.5 99 98.5 99.5 140 139.5 140.5 10 1100 0.035

  6. Upper & Lower bounds Find the upper & lower bounds of these numbers which are rounded to 2 significant figures : LowerUpper 38 37.5 38.5 99 98.5 99.5 140 139.5 140.5 10 9.95 10.05 1100 0.035

  7. Upper & Lower bounds Find the upper & lower bounds of these numbers which are rounded to 2 significant figures : LowerUpper 38 37.5 38.5 99 98.5 99.5 140 139.5 140.5 10 9.95 10.05 1100 1050 1150 0.035

  8. Upper & Lower bounds Find the upper & lower bounds of these numbers which are rounded to 2 significant figures : LowerUpper 38 37.5 38.5 99 98.5 99.5 140 139.5 140.5 10 9.95 10.05 1100 1050 1150 0.035 0.0345 0.0355

  9. Notation The best notation to use for upper & lower bounds is this : If a number (say x) is 42 when rounded to 2 sf’s, then …… 41.5 ≤ x < 42.5 The lower bound = 41.5 The upper bound = 42.5 No equals sign x could equal 41.5

  10. Using rounding appropriately Example The height of 4 people is measured to 3 sf’s (in cm) : 141 150 165 153 Calculate the mean.

  11. Using rounding appropriately The mean is (141 + 150 + 165 + 153) / 4 = 152.25

  12. Using rounding appropriately The mean is (141 + 150 + 165 + 153) / 4 = 152.25 However, as the data was rounded to 3sf’s, it is appropriate to do the same with the answer.

  13. Using rounding appropriately The mean is (141 + 150 + 165 + 153) / 4 = 152.25 However, as the data was rounded to 3sf’s, it is appropriate to do the same with the answer. So the mean is 152 cm.

  14. Finding bounds on answers Example A rectangle is measured as follows : What are the biggest and smallest possible values for the area? 24cm ± 0.5cm 16cm ± 0.5cm

  15. Finding bounds on answers Biggest value = 24.5 x 16.5 = 404.25 Smallest value = 23.5 x 15.5 = 364.25 Therefore : 364.25 ≤ Area < 404.25

  16. Question Practice All on page 238 • Q1 parts a to d only • Q2 • Extension Q3

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