Name of Lecturer: Mr. J.Agius LESSON 24. Percentages and their Applications. Approximations

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1 24.1 Rounding Whole Numbers LESSON 24 Percentages and their Applications Approximations We have seen that it is sometimes unnecessary and often impossible to give exact values. In the case of measurements this is particularly true. However, we do need to know the degree of accuracy of an answer. For example, if a manufacturer is asked to make screws that are about 12½ cm long, he does not know what is acceptable as being about 12½ cm long! But if he is asked to make them 12.5cm long correct to one decimal place, he knows what tolerances to work to. Whole numbers are divided into units, tens, hundreds, thousands, etc. When we are told to approximate to the nearest 10 we look at the units. If there are 5 or more units you add one to the tens. If there are less than 5 units you leave the tens alone. Similar rules apply to rounding off to the nearest 100 (look at the tens); to the nearest 1000 (look at the hundreds); and so on. Example 24A The attendance at a pop concert was 12134, the exact number of tickets sold can be rounded to the nearest ten, hundred, thousand, and so on To the nearest ten: To the nearest hundred: To the nearest thousand To the nearest hundred in general can be used for catering. To the nearest thousand in general can be used by newspaper reporter. Example 24B Round the measurement 555mm: a) to the nearest 10mm b) to the nearest 100mm 555mm is exactly halfway between 550mm and 560mm. When rounding to the nearest 10mm, 555mm rounds upwards to become 560mm. 555mm is between 500mm and 600mm, but nearer 600mm. When rounding to the nearest 100mm, 555mm becomes 600mm. Learning Outcome 1 Numerical Calculations Page 120

2 Exercise 24A 1. Round off each of the following value to a) the nearest ten b) the nearest hundred c) the nearest thousand Nearest ten Nearest Hundred Nearest thousand i) 2479 ii) iii) iv) m 2. The attendance at an athletics meeting was Write this figure to the nearest During the summer season the number of visitors to a heritage centre was Write this figure to the nearest The estimated cost of a school extension is Write this estimate to the nearest Give an approximate answer for each number below. a) James has a flock of 142 chickens. b) Mrs Wilson sold 306 portions of fish and chips. c) Asif needed 6318 bricks to build his new bungalow. d) A crowd of spectators watched Chelsea last night. e) A pop group earned in a year. Learning Outcome 1 Numerical Calculations Page 121

3 6. Liners Launched Length Tonnage Speed Queen Elizabeth ,029 ft 83, knots Queen Mary ,019 ft 80, knots New P&O cruise liner (1994-5) 850 ft 67, knots QE ft 65, knots United States ft 53, knots Canberra ft 45, knots For each of these liners, round: a) the lengths to the nearest ten feet b) the tonnages to the nearest hundred tonnes c) the speeds to the nearest ten knots. Liners Launched Length Tonnage Speed Queen Elizabeth Queen Mary New P&O cruise liner QE2 United States Canberra 7. The table gives the areas and populations of five European Union states. Country Area (km 2 ) Population Greece Italy Netherlands Germany Ireland Round: a) The areas to the nearest thousand km 2. b) The populations to the nearest hundred thousand. Country Area (km 2 ) Population Greece Italy Netherlands Germany Ireland Learning Outcome 1 Numerical Calculations Page 122

4 24.2 Rounding to a Number of Decimal Places There are times when you work sometimes out on your calculator and the number fills the whole display. The answer is far more accurate than you need. Instead of using all the digits you can round the number to a given number of decimal places. To correct to two decimal places (d.p) we look at the third decimal place. If it is 5 or larger, we add 1 to the figure in the second decimal place. If it is less than 5, we do not alter the figure in the second decimal place. Example 24C Find correct to a) 3 d.p. b) 2.d.p. c) 1d.p. Answer a) = correct to 3 d.p. b) = 0.08 correct to 2 d.p. c) = 0.1 correct to 1 d.p. Note; We begin to count decimal places from the decimal point and the answer should have the same number of decimal places you are correcting for. All the numbers after that decimal point are converted to zero automatically. Exercise 24C Round off each of the following values correct to a) 3 d.p. b) 2 d.p. c) 1d.p. 1) Ans. a) Ans. b) Ans. c) 2) Ans. a) Ans. b) Ans. c) 3) Ans. a) Ans. b) Ans. c) 4) Ans. a) Ans. b) Ans. c) Learning Outcome 1 Numerical Calculations Page 123

5 Mixed Exercises 1) The value of is Write this value correct to a) 1 decimal place b) 2 decimal places c) 3 decimal places 2) Use your calculator to find the square root of 20. Write this value correct to a) 1 decimal place b) 2 decimal places c) 3 decimal places 3) How many decimal places do you give if your answer is correct to the nearest a) tenth? b) hundredth? 4) For each of these, write down your estimate of the reading to the nearest hundredth, and then write the reading correct to the nearest tenth. a) b) ) Write these fractions as decimals correct to 3 decimal places. a) b) c) d) 6) Calculate 12.6% of 43.8, giving your answer correct to 2 decimal places. Measure the length and width of this rectangle in centimetres giving your answer correct to 1 decimal place. 7) a) 8) b) Use these values to calculate the area of the rectangle giving your answer correct to 1 decimal place. Work out the mean of these numbers giving your answer correct to 2 decimal places. 4, 4, 5, 7, 8, 12, 15 9) A circle has radius 7.3m. Using = 3.14 calculate, correct to 1 decimal place, a) Its circumference b) Its area. Learning Outcome 1 Numerical Calculations Page 124