Presentation on theme: "Physical quantities and their measurements"— Presentation transcript:
1 Physical quantities and their measurements Measurement of length and volumeInstruments of measurementLeast count and Precision of an instrumentSignificant figuresUncertainty in a measurementAccuracy and errors – Systematic and random
2 Measuring Volume of a liquid http://www. chem. tamu Beaker graduated cylinder buret
3 Beaker – least count and significant figures The smallest division is 10 mL, so we can read the volume to 1/10 of 10 mL or 1 mL. The volume we read from the beaker has a reading error of 1 mL.The volume in this beaker is mL. You might have read 46 mL; your friend might read the volume as 48 mL. All the answers are correct within the reading error of 1 mL.So, How many significant figures does our volume of mL have? Answer - 2! The "4" we know for sure plus the "7" we had to estimate.
4 Graduated cylinderFirst, note that the surface of the liquid is curved. This is called the meniscus. This phenomenon is caused by the fact that water molecules are more attracted to glass than to each other (adhesive forces are stronger than cohesive forces). When we read the volume, we read it at the BOTTOM of the meniscus.The smallest division of this graduated cylinder is 1 mL. Therefore, our reading error will be 0.1 mL or 1/10 of the smallest division. An appropriate reading of the volume is mL. An equally precise value would be 36.6 mL or 36.4 mL.How many significant figures does our answer have? 3! The "3" and the "6" we know for sure and the "5" we had to estimate a little.
5 BuretThe smallest division in this buret is 0.1 mL. Therefore, our reading error is mL. A good volume reading is mL. An equally precise answer would be mL or mL.How many significant figures does our answer have? 4! The "2", "0", and "3" we definitely know and the "8" we had to estimate.
6 Conclusion – sf and precision The number of significant figures is directly linked to a measurement. If a person needed only a rough estimate of volume, the beaker volume is satisfactory (2 significant figures), otherwise one should use the graduated cylinder (3 significant figures) or better yet, the buret (4 significant figures).So, does the concept of significant figures deal with precision or accuracy? Hopefully, you can see that it really deals with precision only.
7 Rulers Meter rule in inch, centimetre and millimetre Half metre rule Precision is how fine of a measurement that the measuring instrument is marked off for.
11 Least CountThe least count is the smallest subdivision marked on a measuring instrument.Determine the least count of your measuring stick.Record the numerical value of the least count and the unit of measurement.Example: A meter stick is divided into 100 equal divisions and numbered. Each of these numbered divisions is called 1 cm. ('one centimeter' means 'one one-hundredth' of a meter). Each centimeter is further divided into 10 equal divisions. This is the smallest subdivision on the meter stick.
13 Other instruments to measure length Micrometer screw gaugeVernier calipers
14 Rules for Working with Significant Figures: Leading zeros are never significant. Imbedded zeros are always significant. Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.Addition or Subtraction: The last digit retained is set by the first doubtful digit.Multiplication or Division: The answer contains no more significant figures than the least accurately known number.
15 Exact and inexact numbers example: There are exactly 12 eggs in a dozen.example: Most people have exactly 10 fingers and 10 toes.
16 inexact numbers:example: any measurement. If I quickly measure the width of a piece of notebook paper,I might get 220 mm (2 significant figures).If I am more precise, I might get 216 mm (3 significant figures).An even more precise measurement would be mm (4 significant figures).
19 Significant digits3 sig. digs..5 sig. digs.1 sig. dig.2 sig. digs.4 sig. digs.
20 Rules for Working with Significant Figures:1 Leading zeros are never significant. Imbedded zeros are always significant. Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.
21 Rules for Working with Significant Figures: 2 Addition or Subtraction: The last digit retained is set by the first doubtful digit.Multiplication or Division: The answer contains no more significant figures than the least accurately known number.
22 Rounding off Addition or Subtraction: The last digit retained is set by the first doubtful digit
23 Addition or Subtraction: The last digit retained is set by the first doubtful digit
24 Multiplication or Division:The answer contains no more significant figures than the least accurately know number.
25 Multiplication or Division: The answer contains no more significant figures than the least accurately known number.
26 Significant figures and electronic calculators . For example, dividing 5.0 by 1.67 on a calculator may give the following answer:5.0 / 1.67=The correct answer, 3.0, has only two significant figures, as in the least accurate number (5.0) in the problem. All other digits displayed by the calculator are insignificant.
27 Rounding offLet's round off 64,492 to: (a) 1 significant figure which is 60,000 (b) 2 significant figures which is 64,000 (c) 3 significant figures which is 64,500 (d) 4 significant figures which is 64,490 (e) 5 significant figures which is 64,492
28 rounding off to given significant figures When rounding off numbers to a certain number of significant figures, do so to the nearest value.example: Round to 3 significant figures: x 104 (Answer: 2.35 x 104)example: Round to 2 significant figures: x 103 (Answer: 1.6 x 103)
29 What happens if there is a 5? There is an arbitrary rule: If the number before the 5 is odd, round up.If the number before the 5 is even, let it be. The justification for this is that in the course of a series of many calculations, any rounding errors will be averaged out.example: Round to 2 significant figures: 2.35 x 102 (Answer: 2.4 x 102)example: Round to 2 significant figures: 2.45 x 102 (Answer: 2.4 x 102)Of course, if we round to 2 significant figures: x 102, the answer is definitely 2.5 x 102 since x 102 is closer to 2.5 x 102 than 2.4 x 102.
30 QUIZ:Question 1Give the correct number of significant figures for 4500, 4500., ,Question 2Give the answer to the correct number of significant figures: = ?
31 QuestionsQuestion 3Give the answer to the correct number of significant figures: = ?Question 4Give the answer to the correct number of significant figures: (1.3 x 103)(5.724 x 104) = ?
32 QuestionsQuestion 5Give the answer to the correct number of significant figures:(6305)/(0.010) = ?
33 Example Significant figures Number Exponential expression Significant figures560, X two(The zeros show only the location of the decimal point.)560, X 105 six (The decimal point in the original number shows that all the zeros are significant.)30, X four(The first zero is between two digits and is significant. The last shows only the location of the decimal point.)
34 X three(The first two zeros show the location of the decimal; they are not significant. The last one does not show the location of the decimal point; it reports a measurement and therefore is significant.)
35 Errors Random Errors: Errors that can not be predicted. Systematic Errors: Errors which are the same for each measurement
36 Precision and accuracy Poor Precision -> the hits are not near each otherPoor Accuracy -> the hits are not near their intended targetGood Precision -> all the hits are close to each otherGood Accuracy -> all the hits are near their intended targetGood Precision -> all the hits are close to each otherPoor Accuracy -> the hits are not near their intended target
37 Precision: Small random error Accurate: Small systematic error
38 Absolute uncertainty Size of an error and its units 30m tape measure has an error of ±0.5cmSo the Absolute error is30±0.005 m
39 Fractional uncertainty Absolute uncertainty / measurement30m tape measure has an error of ±0.5cmFractional Uncertainty = 0.005/30
40 Percentage uncertainty Fractional uncertainty x 100%Therefore0.005/30 x 100% = 0.017%
42 Task1.)Use your ruler to measure the length of your desk. State the uncertainty in your measurement.
43 Multiplication and Division 5.6 ±0.5m x 2.6 ±0.5m = 15 ±??m 0.5 / 5.6 = / 2.6 = Sum of relative errors = Absolute error = x 15 = 4.2m FINAL ANSWER = 15 ±4 m
44 Example QuestionThe length of a piece of paper is measured as 297± 1mm. Its width is measured as 209± 1mmWhat is the fractional uncertainty in its lengthWhat is the percentage uncertainty in its length?What is the area of one side of the piece of paper? State your answer with its uncertainty
45 2.) What is the area of your desk? RememberA/A = L/L + W/W
46 Example Question 2A Voltmeter has a reading of 2.00±0.05 V, a miliammeter reads 3.3±0.1 mA Estimate the Resistance and state your uncertainties.
47 Question 3What do the terms systematic and random errors mean?