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Rounding

2. 1. 1.4. 2. 1. 1.5. Rounding. Round to the nearest whole number. 1.4. 1.4 is clearly closer to 1 than 2 so it rounds to 1. Round to the nearest whole number. 1.5. Technically 1.5 is in the middle, but we always round up 0.5 to the next whole number in this case 2 (Integer).

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Rounding

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  1. 2 1 1.4 2 1 1.5 Rounding Round to the nearest whole number 1.4 1.4 is clearly closer to 1 than 2 so it rounds to 1 Round to the nearest whole number 1.5 Technically 1.5 is in the middle, but we always round up 0.5 to the next whole number in this case 2 (Integer) Summary to round to the place value required look to the number to the right: 4 or less - the number stays the same (round down) 5 or more - the number increases by 1 (round up) DO NOT CHANGE THE PLACE VALUE

  2. Rounding Examples: 6 5 2 9 3 . 4 Look to the figure to the right It is 4 or less so round down Round to the nearest integer 65293 Look to the figure to the right It is 4 or less so round down Round to the nearest ten 65290 Look to the figure to the right It is 5 or more so round up Round to the nearest hundred 65300 Look to the figure to the right It is 4 or less so round down Round to the nearest thousand 65000 Round to the nearest ten thousand Look to the figure to the right It is 5 or more so round up 70000

  3. Rounding This also works for decimals This number is said to have one decimal place (1 d.p.) Definition: 7.4 This number is said to have two decimal places (2 d.p.) 10.36 This number is said to have three decimal places (3 d.p.) 8.462 etc. Examples: 9.8 6 2 8 7 Look to the figure to the right It is 5 or more so round up Round to 1 decimal place 9.9 Look to the figure to the right It is 4 or less so round down Round to 2 d.p. 9.86 Look to the figure to the right It is 5 or more so round up Round to 3 d.p. 9.863

  4. 6.8 6.9 7.0 7.1 Rounding Harder Example 6.99 Round to 1 d.p. It is easier to see this on a number line The first decimal place is tenths so if we look in increments of one tenth 6.99 6.99 is now clearly closer to 7.0 than 6.9 so we have to round up to 7.0

  5. Rounding Now answer these: Round these measurements to 1 decimal place (that is, to the nearest millimetre). a) 18.67 cm b) 8.38 cm c) 68.23 cm d) 0.678 cm e) 0.4545 cm 6 Round these masses to 3 decimal places (that is, to the nearest gram). a) 1.7683 kg b) 48.2467 kg c) 8.9247 kg d) 0.052905 kg e) 0.00035679 kg 18.7 cm 8.4 cm 68.2 cm 0.7 cm 0.5 cm 1.768 kg 48.247 kg 8.925 kg 0.053 kg 0.000 kg

  6. Rounding Rounding to the most significant figure 4 5 6 2 Which is the figure that describes the number the best? The thousand column has the most significant figure If I wanted to describe this number using only one non zero figure (1.s.f.) it would be 5000 The hundred is the second most significant figure If I wanted to describe this number using two non zero figures (2 s.f.) it would be 4600 (round up because the figure next to it is a 6) Example 8624 write this number to: 1 s.f. 9000 2 s.f. 8600 4 s.f. 8624 3 s.f. 8620

  7. Rounding Now answer these: • 1. Round these numbers to one significant figure. • 326 b) 589 c) 3245 • Round these numbers to two significant figures. • d) 9999 e) 9099 f) 9950 • 2. Round these numbers to one significant figure. • 4.826 b) 0.4826 c) 0.04826 d) 0.004826 • Round these numbers to two significant figures. • e) 0.0004826 f) 0.00004826 3000 300 600 10000 10000 9100 0.5 5 0.05 0.005 0.00048 0.000048

  8. 62.3 x 78.4 124 60 x 80 120 4800 120 Estimating If I went to the shop and wanted 5 litres of milk and I saw the price at £0.96 I would think that I would need about £5 I have rounded £0.96 to 1 s.f. £1 and multiplied it by 5 to £5 Why? Estimating can be done simply by rounding to the nearest significant figure: Examples Round each number to 1 s.f. 9.58 x 2.73 10 x 3 Estimated answer 30 Actual answer 26.1534 Round each number to 1 s.f. Calculate the Numerator first Estimated answer 400 Actual answer 39.3897

  9. 8 2 = 4 =96 0.3 or 960 3 = 320 Estimating Now try these 0.2 x 6 = 1.2 8 + 5 = 13 90 x 6 = 540 = 1700 0.3 0.3 20 x (8-4) = 80 =50 =240 =8 =640 =100 =81 =280

  10. 60 60 80 80 90 90 Upper & Lower Bounds What could be the highest this number could be if it has already been rounded to the nearest 10? 70 74 would be rounded down to 70 but 75 would be rounded up to 80 Therefore the highest the number could be before rounding is 74 What could be the lowest this number could be if it has already been rounded to the nearest 10? 70 65 would be rounded up to 70 but 64 would be rounded down to 60 Therefore the lowest the number could be before rounding is 65

  11. Upper & Lower Bounds Now try these • 1.Each of these quantities is rounded to the nearest whole number • of units. Write down the minimum and maximum possible size of each quantity. • 26 g b) 4 cm c) 225 m • d) 13 litres e) 33 kg f) £249 4.4 cm 3.5 cm 225.4 m 224.5 m 26.4 g 25.5 g 12.4 g 12.5 g 33.4 kg 32.5 kg £249.50 £248.49 3.A packet weighs 2 kg, correct to the nearest 100 g. What is the maximum possible weight? 2.049 kg 5. The weight of a toffee is 5 g correct to the nearest half gram. What is the minimum possible weight of one toffee? 4.75 g

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