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3. Error in Measurement     cm 1 2 3 0 The six small strips of wood were measured using the ruler shown. Which of the strips shown are measured as 2 cm to the nearest cm. a b c d e e All 4 strips that measured 2 cm were within the range 1.5 to 2.5 cm.

4. Error in Measurement     cm 0.10.2 0.3 0 The six small strips of wood were measured using the ruler shown. Which of the strips shown are measured as 2 cm to the nearest cm. a b c d e e All 4 strips that measured 2 cm were within the range 1.5 to 2.5 cm. Had the strips been (very small) and measured on another scale as 0.2 cm to the nearest tenth of a centimetre the range of measurements would have been 0.15 to 0.25 cm Continuing in this way we can see that any measurement can only be an approximation accurate to  1/2 the stated degree of accuracy centred on the measurement.

5. Error in Measurement Remember: All measurements are approximations. They are accurate to  1/2 the stated degree of accuracy centred on the measurement. A half marathon race is won in a time of 1hr 42 minutes, timed to the nearest minute. Find the longest and shortest possible times that the winner could have taken. Possible error is  ½ a minute, so longest time is 1hr 42 min 30 sec and shortest time is 1 hr 41 min 30 sec. 100 200 300 400 500 600 700 800 900 0 grams 675 g A package is weighed as 675 g to the nearest 25 g. Find the maximum and minimum weight of the package. Possible error is  ½ of 25 g (12.5 g), so the maximum weight is 687.5 g and the minimum weight is 662.5 g. Example Questions

6. Remember: All measurements are approximations. They are accurate to  1/2 the stated degree of accuracy centred on the measurement. Example Questions An athlete jumps a distance of 6.93 m measured to the nearest cm. Find the maximum and minimum distances that he could have jumped Possible error is  ½ cm, so longest distance is 6.935 m and minimum distance is 6.925 m. The temperature of some hot water is measured as 97.7 o F to the nearest tenth of a degree. Find the maximum and minimum temperature for the water. Possible error is  ½ of 0.1 o = 0.05 o. So maximum temperature = 97.75 o F and minimum temperature =97.65 o F. Error in Measurement

7. 100 ml 200 ml 300 ml 400 ml 500 ml Remember: All measurements are approximations. They are accurate to  1/2 the stated degree of accuracy centred on the measurement. Questions Error in Measurement 1 Weight of an egg 64 g (nearest g) Amount of liquid 280 ml (nearest 20 ml) 2 3 Time of a race 23.4 seconds (nearest tenth of a second) Find the maximum and minimum measurements for the situations shown below. Maximum 64.5 g Minimum 63.5 g Maximum 23.45 seconds Minimum 23.35 seconds Maximum 290 ml Minimum 270 ml

8. Remember: All measurements are approximations. They are accurate to  1/2 the stated degree of accuracy centred on the measurement. Questions Error in Measurement 4 Oil in a barrel 56.68 litres (nearest cl) A temperature of 60 o F (nearest 2 degrees) 5 6 Height of Eiffel Tower 320 m (nearest metre) Find the maximum and minimum measurements for the situations shown below. Maximum 56.685 litres Maximum 320.5 m Minimum 319.5 m Maximum 61 o F Minimum 59 0 F Oil Maximum 56.675 litres