MEASUREMENT Limits of Accuracy

1. MEASUREMENT • Limits of Accuracy

2. Display of your answer When writing your answer you can be asked to display it different ways, and sometimes you are not asked, so you need to make the best judgment decision. Significant figures (sf) Decimal place (dp) Standard form Rounding to the nearest … It is very important that you read the questions properly for the appropriate information.

3. Practice The length of a piece of timber is 5.3659m in length Write this Round to the nearest m To the nearest cm In mm to 2 significant figures In m to 2dp In standard form in mm (1dp, and also 2sf)

4. Limits of Accuracy • Measurements are never exact. There is a limit to the accuracy with which a measurement can be made. • The limits of accuracy of measurement refers to the range of values within which the true value of the measurement lies. • The range of values is defined by an upper limit and a lower limit.

5. Limits of Accuracy • To find the upper limit, add 5 to the nearest significant place. • To find the lower limit, minus 5 to the nearest significant place. e.g. The distance to Bluff on a signpost reads 17 km. The upper limit is 17 + 0.5 = The lower limit is 17 – 0.5 = Therefore the limits of accuracy are 16.5 km ≤ Bluff ≤ 17.5 km

6. e.g. From home to school it is 27.5 km. What are the limits of accuracy for my distance to school? The upper limit is 27.5 + 0.05 = 27.55 km The lower limit is 27.5 – 0.05 = 27.45 km Therefore the limits of accuracy are: 27.45 km ≤ Distance ≤ 27.55 km

7. e.g. At the Otago vs Auckland game at Carisbrook it was reported that 28500 people attended. Give the limits of accuracy for the number of people attending the game? The upper limit is 28500 + 50 = 28550 The lower limit is 28500 – 50 = 28450 Therefore the limits of accuracy are: 28450 ≤ People ≤ 28550

8. Practice 67.5 mm ≤ x ≤ 68.5 mm Give the limits of accuracy for these measurements: 1.) 68 mm 2.) 397 mm 3.) 4 seconds 4.) 50 g 5.) 5890 kg 6.) 820 cm 7.) 92 kg 8.) 89.1° 396.5 mm ≤ x ≤ 397.5 mm 3.5 seconds ≤ x ≤ 4.5 seconds 45 g ≤ x ≤ 55 g 5885 kg ≤ x ≤ 5895 kg 815 cm ≤ x ≤ 825 cm 91.5 kg ≤ x ≤ 92.5 kg 89.05° ≤ x ≤ 89.15°

9. Rounding It is sometimes required that we provide an answer whereby we should sensibly round it. • Example • Sam bought a trailer load of firewood. He wants to know the weight of the load. Sam counted blocks of wood as he loaded them. He has 563 blocks. Then he picks up an average size block and weights it. It is 2.38kg. • Estimate the weight of the load on the trailer. Round sensibly. • 563 x 2.38 = 1339.94 kg • Sensible Answer 1300 kg (to the nearest 100 kg) • Alternative Answer 1.3 t (to the nearest tonne)

10. Practice • Marianne used a tape to measure the length of her garden (the tape went over some bumps on the ground). She read off 67.35m. What measurement should Marianne write down? • …………m (to the nearest ………..) • The area of Fiordland National Park is 12519 km2. • Wendy wrote this measurement as 12500 km2. • How did Wendy round? to the nearest ………….…… • About nine hundred drops of water filled the measuring jug to 100 mL. What is the volume of 1 drop? Round sensibly. • …………mL (to the nearest ………..) m 67 100 km2 mL 0.1