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“ Scientific Measurement ”

Action Plan. “ Scientific Measurement ”. Presented By, Ghufran Ali DA SKBZ College. Contents:. Measurement and uncertainty Scientific and standard notations Accuracy and precession Error Significant figures and rounding the data Unit system Conversion of units. Learning objectives.

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“ Scientific Measurement ”

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  1. Action Plan “Scientific Measurement” Presented By, Ghufran Ali DA SKBZ College

  2. Contents: Measurement and uncertainty Scientific and standard notations Accuracy and precession Error Significant figures and rounding the data Unit system Conversion of units

  3. Learning objectives

  4. Short term goals: Measurement helps to understand each and every topic regarding physical science easily. To enhance the critical and logical thinking. To analyze the use of units in daily life.

  5. Long term goals: It provides basic knowledge so it will be very useful at higher level. Growth of engineering and technology.

  6. Measurements and Their Uncertainty • OBJECTIVES: • Convert measurements to scientific notation. • Distinguish among accuracy, precision, and error of a measurement • Determine the number of significant figures in a measurement and in a calculated answer.

  7. Measurements • We make measurements every day: buying products, sports activities, and cooking • Qualitative measurements are words, such as heavy or hot • Quantitative measurements involve numbers (quantities), and depend on: • The reliability of the measuring instrument • the care with which it is read – this is determined by YOU! • Scientific Notation • Coefficient raised to power of 10 (ex. 1.3 x 107)

  8. Accuracy, Precision, and Error • It is necessary to make good, reliable measurements in the lab • Accuracy – How close a measurement is to the true value • Precision – How close the measurements are to each other (reproducibility)

  9. Precision and Accuracy Precise, but not accurate Neither accurate nor precise Precise AND accurate

  10. Accuracy, Precision, and Error • Accepted value The correct value based on reliable references. • Experimental value The value measured in the lab

  11. Accuracy, Precision, and Error • Error = accepted value – exp. value • Can be positive or negative • Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100% | error | accepted value x 100% % error =

  12. Why Is there Uncertainty? • Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places • Which of the balances below has the greatest uncertainty in measurement?

  13. Significant Figures in Measurements • Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated. • Measurements must be reported to the correct number of significant figures.

  14. Which measurement is the best? What is the measured value? What is the measured value? What is the measured value?

  15. Rules for Counting Significant Figures Non-zerosalways count as significant figures: 3456has 4significant figures

  16. Rules for Counting Significant Figures Zeros Leading zeroes do not count as significant figures: 0.0486 has 3 significant figures

  17. Rules for Counting Significant Figures Zeros Captive zeroes always count as significant figures: 16.07has 4 significant figures

  18. Rules for Counting Significant Figures Zeros Trailing zerosare significant only if the number contains a written decimal point: 9.300 has 4 significant figures

  19. Rules for Counting Significant Figures Two special situationshave an unlimited number of significant figures: • Counted items • 23 people, or 425 thumbtacks • Exactly defined quantities • 60 minutes = 1 hour

  20. Sig Fig Practice #1 How many significant figures in the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs These all come from some measurements 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 mL  2 sig figs This is a counted value 5 dogs  unlimited

  21. Significant Figures in Calculations • In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. • Ever heard that a chain is only as strong as the weakest link? • Sometimes, calculated values need to be rounded off.

  22. Rounding Calculated Answers • Rounding • Decide how many significant figures are needed (more on this very soon) • Round to that many digits, counting from the left • Is the next digit less than 5? Drop it. • Next digit 5 or greater? Increase by 1

  23. Rounding Calculated Answers • Addition and Subtraction • The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem.

  24. Rounding Calculated Answers • Multiplication and Division • Round the answer to the same number of significant figures as the least number of significant figures in the problem.

  25. Rules for Significant Figures in Mathematical Operations • Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 =12.76 13 (2 sig figs)

  26. Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5872.786 lb·ft 2.9561 g/mL 2.96 g/mL 1.030 g x 2.87 mL

  27. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 =18.734  18.7 (3 sig figs)

  28. Sig Fig Practice #3 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL

  29. Unit System Metric System (M.K.S) (International System of Units) English System (F.P.S)

  30. Metric System • Measurements depend upon units that serve as reference standards • The standards of measurement used in science are those of the Metric System

  31. International System of Units (SI) • Metric system is now revised and named as the International System of Units (SI), as of 1960 • SI units are used throughout the world except in the United States and some of the United Kingdom. • It has simplicity, and is based on 10 or multiples of 10

  32. The Fundamental SI Units

  33. SI vs English • The “English” system is what we are probably more familiar with. English units for the same measures are: • Length: inches/feet/yards/miles • Mass: ounces/pounds/tons • Volume: fluid ounce/cups/quarts/gallons • Temperature: Fahrenheit/Celsius

  34. Why use SI? • There is one key advantage of SI over English. • Metric (SI) units work in 10s, therefore it is very easy to convert from big units to small units and vice versa. • English units are not easy to convert. Can you easily convert one mile to inches?

  35. Teaching prefixesLearn the 20 regular prefixes by counting . Change them by jumping the decimal point 3 places .

  36. SI Prefixes

  37. Length • In SI, the basic unit of length is the meter (m) • Length is the distance between two objects – measured with ruler • We make use of prefixes for units larger or smaller

  38. Conversion Problems • OBJECTIVE: • Construct conversion factors from equivalent measurements. • Apply the techniques of dimensional analysis to a variety of conversion problems. • Solve problems by breaking the solution into steps. • Convert complex units, using dimensional analysis.

  39. Conversion factors • Equivalence statements always have this relationship: big # small unit = small # big unit 1000 mm = 1 m

  40. What are the units?! • Length: Length is measured in METERS • Mass: Mass is measured in GRAMS • Volume: Volume is measured in LITERS • Temperature: Temperature is measured in KELVIN (Celsius is sometimes used instead)

  41. Moving between units • To change from one unit size or type to another is called a “conversion”. To help us learn conversions you will want to familiarize yourself with this saying: “King Henry Died _ drinking chocolate milk”

  42. Say What? • King: Kilo (meaning 1000) • Henry: Hecto (meaning 100) • Died: Deca (meaning 10) • _ : the base unit (1) • drinking: deci (meaning 1/10) • chocolate: centi (meaning 1/100) • milk: milli (meaning 1/1000)

  43. We are going to use our knowledge about multiplying and dividing by 100 to convert centimetres to metres and to convert metres to centimetres.

  44. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

  45. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

  46. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

  47. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

  48. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

  49. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

  50. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- ÷100

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