2. Section 1.2 Section 1.2 Measurement In this section you will: Section 1.2 1 ●Distinguish between accuracy and precision. ●Determine the precision of measured quantities.

3. Section 1.2 Section 1.2 Measurement A measurement is a comparison between an unknown quantity and a standard. Measurements quantify observations. Careful measurements enable you to derive the relationship between any two quantities. What is a Measurement? Section 1.2 2

4. Section 1.2 Section 1.2 Measurement When a measurement is made, the results are often reported with uncertainty. Therefore, before fully accepting new data, other scientists examine the experiment, looking for possible sources of errors, and try to reproduce the results. A new measurement that is within the margin of uncertainty confirms the old measurement. Comparing Results Section 1.2 3

5. Section 1.2 Section 1.2 Measurement Precision Versus Accuracy Click image to view the movie. Section 1.2 4

6. Section 1.2 Section 1.2 Measurement To assure precision and accuracy, instruments used to make measurements need to be used correctly. This is important because one common source of error comes from the angle at which an instrument is read. Techniques of Good Measurement Section 1.2 5

7. Section 1.2 Section 1.2 Measurement To understand this fact better, observe the animation on the right carefully. Techniques of Good Measurement Section 1.2 5

8. Section 1.2 Section 1.2 Measurement Scales should be read with one’s eye straight in front of the measure. If the scale is read from an angle, as shown in figure (b), you will get a different, and less accurate, value. Techniques of Good Measurement (a) (b) Section 1.2 6

9. Section 1.2 Section 1.2 Measurement The difference in the readings is caused by parallax, which is the apparent shift in the position of an object when it is viewed from different angles. Techniques of Good Measurement Section 1.2 6

10. Section 1.2 Section 1.2 Section Check Ronald, Kevin, and Paul perform an experiment to determine the value of acceleration due to gravity on Earth (which most scientists agree is about 980 cm/s 2 ). The following results were obtained: Ronald — 961 ± 12 cm/s 2, Kevin — 953 ± 8 cm/s 2, and Paul — 942 ± 4 cm/s 2. Determine who has the most accurate and precise value. Question 1 Section 1.2 7

11. Section 1.2 Section 1.2 Section Check Question 1 A.Kevin got the most precise and accurate value. B.Ronald’s value is the most accurate, while Kevin’s value is the most precise. C.Ronald’s value is the most accurate, while Paul’s value is the most precise. D.Paul’s value is the most accurate, while Ronald’s value is the most precise. Section 1.2 7

12. Section 1.2 Section 1.2 Section Check Answer 1 Reason: Ronald’s answer is closest to 980 cm/s 2. Hence, Ronald’s result is the most accurate. However, Paul’s error is only ±4 cm/s 2. Hence, Paul’s result is the most precise. Section 1.2 8

13. Section 1.2 Section 1.2 Section Check What is the precision of an instrument? Question 2 A.the smallest divisions marked on the instrument B.the least count written on the instrument C.one-half the least count written on the instrument D.one-half the smallest division written on the instrument Section 1.2 9

14. Section 1.2 Section 1.2 Section Check Answer 2 Reason: Precision depends on the instrument and the technique used to make the measurement. Generally, the device with the finest division on its scale produces the most precise measurement. The precision of a measurement is one-half of the smallest division of the instrument. Section 1.2 10

15. Section 1.2 Section 1.2 Section Check A 100-cm long rope was measured with three different measuring tapes. The answer obtained with the three measuring tapes were: 1 st measuring tape — 99 ± 0.5 cm, 2 nd measuring tape — 98 ± 0.25 cm, and 3 rd measuring tape — 99 ± 1 cm. Which measuring tape is the most precise? Question 3 A.1 st measuring tape B.2 nd measuring tape C.3 rd measuring tape D.Both measuring tapes 1 and 3 Section 1.2 11

16. Section 1.2 Section 1.2 Section Check Answer 3 Reason: Precision depends on the instrument. The 2 nd measuring tape has an error of only ±0.25 cm and is therefore the most precise. Section 1.2 12

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