ESTIMATION AND APPROXIMATION
TIP: When doing these sort of problems, remember:
a) When you round a number to a number of significant figures (e.g. 2 s.f., 3 s.f. etc.), you start counting the significant figures as any which are not 0 from the left.
e.g. 0.000628314 to 2 s.f. is 0.00063
8793 to 3 s.f. is 8790
b) When you round a number to a number of decimal places (2 d.p. 3 d.p. etc.), you coutn the number of decimal places you need and look at the next digit to the right. If this digit is less than 5 round down, if its 5 or more round up.
e.g. 23.65789 to 2 .d.p. is 23.66
c) Things can be measured with inaccurate equipment, or a degree of tolerance is allowed in measuring. If you measure something which is correct to a given unit (where units could be cm, mm, kg etc.) the true value could be anywhere in a range between half a unit below (called the greatest lower bound) and half a unit above (called the least upper bound).
e.g. a line measured as 156cm correct to the nearest cm could really be anything between 155.5 cm and 156.5 cm.
d) To estimate answers round all numbers to 1 significant figure.
e) Be very wary of exam questions - remember to re-read the end of the question after working out the answer. The final part of the question will often say things like "give your answer to 3 s.f." etc. Normally a mark is given just for remembering to do this!
Solve the following:
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1. A rectangular carpet has a length of 6.4 m and a width of 3.5 m, where each measurement is measured to the nearest 0.1m. Calculate:
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2. There are approximately 1.853 km in a nautical mile. Estimate how many kilometres there are in 190 nautical miles giving your answer to 1 s.f.
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3. Show how you would estimate the answer to the following expression without using a calculator: 9.75 + 30.2
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4. Perform the calculation 12.657 x 8.972 (a) Give your answer correct to 3 d.p.
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5. In a 1500 metre race a runner's time was calculated to be 4 minutes 12.43 seconds. If race times are measured to the nearest 0.01 seconds, write down the range of times between which the runner's exact time lies. |
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6. A carton of orange juice has a square base where each side is 6.7 cm and a height of 16.3 cm. The measurements are correct to an accuracy of 1 decimal place. (a) If a factory needs to make 3,000 of these cartons in a production run, how much juice must be available to be sure of filling all the cartons? (b) What is the maximum amount of cartons that could be made from the total amount of juice in your answer to (a)?
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7. A brochure in the estate agents gives the measurements of the sitting room in a house as 10.8m by 8.2m. The measurements are taken to the nearest 10cm. (a) What is the maximum area of the room? |
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8. A rectangular field is 260m by 180m. If the measurements are taken to the nearest 5 metres, what is the maximum perimeter of the field? |