Topic-1.2_UNITS-MEASUREMENTS_PART-2.pdf

Click to edit Master title style UNITS AND MEASUREMENTS G e n e r a l P h ys i c s 1 1 Click to edit Master title style MEASUREMENTS Scientific Notation Significant Figures Uncertainty in Measurem...

Click to edit Master title style UNITS AND MEASUREMENTS G e n e r a l P h ys i c s 1 1 Click to edit Master title style MEASUREMENTS Scientific Notation Significant Figures Uncertainty in Measurement Precision and Accuracy 2 2  Lesson Objectives Click to edit Master title style At the end of the lesson, the students will be able to: a) express measurements in scientific notation. b) differentiate accuracy from precision; and c) estimate errors from multiple measurements of a physical quantity using variance. 3 3 Click to edit Notation Scientific Master title style - is a way to express extremely large/ big numbers and small numbers into simpler numbers. 1.57 x 10 5 coefficient exponent base 4 4 Click to edit Notation Scientific Master title style Converting Standard Notation to Scientific Notation 183 000 000 1.83 x 108 4 406 200 4.4062 x 106 0.000000087 8.7 x 10-8 0.0004567 4.567 x 10-4 5 5 Click to edit Notation Scientific Master title style Converting Scientific Notation to Standard Notation 2.85 x 1010 28 500 000 000 1.4567 x 108 145 670 000 4.3354 x 10-7 0.00000043354 5.9 x 10-11 0.000000000059 6 6 Significant Figures Click to edit Master title style Rules in Determining Significant Figures 1) All nonzero digits (1 to 9) are significant. Examples: 145 m 3 SF 12, 938 in 5 SF 135, 112 g 6 SF 7 7 Significant Figures Click to edit Master title style Rules in Determining Significant Figures 2) Zeros to the left of the first non-zero digit are not significant. Examples: 0.045 g 2 SF 0.0001 mm 1 SF 0.12 mL 2 SF 8 8 Significant Figures Click to edit Master title style Rules in Determining Significant Figures 3) Zeros between non-zero digits are significant. Examples: 202 ft 3 SF 2.005 mi 4 SF 2.020002 lbs 7 SF 9 9 Significant Figures Click to edit Master title style Rules in Determining Significant Figures 4) Zeros to the right of a nonzero digit with a decimal point are significant. Examples: 1.00 km 3 SF 9.33000 g 6 SF 11.10 cm 4 SF 1010 Significant Figures Click to edit Master title style Rules in Determining Significant Figures 5) Zeros at the end of a non-zero digit without a decimal point are not significant. Examples: 100 kg 1 SF 10, 000 km 1 SF 255, 000, 000 ft 3 SF 1111 Significant Figures Click to edit Master title style Addition and Subtraction - the number of decimal places in the answer should be the same as the number with the least decimal places among those being added or subtracted. Examples: 2.4067 m 8.90563 g + 3.4 m - 3.21 g + 12.0112 m 5.70 g 17.8 m 1212 Significant Figures Click to edit Master title style Multiplication and Division - the answer should have the same number of significant figures as the number with the least number of significant figures among the numbers being multiplied and divided. Examples: 12.1573 m 12.5678 m x 1.10 m ÷ 4.001 s 13.4 𝐦𝟐 3.141 𝐦Τ𝐬 1313 Uncertainty in Measurement Click to edit Master title style Certain/ Exact Digits – the ones that the measuring instrument can give you. 1414 Uncertainty in Measurement Click to edit Master title style Uncertain Digits – the ones that you estimate. 1515 Uncertainty in Measurement Click to edit Master title style Least Count – the smallest marked division in the measuring instrument. (0.1 cm or 1mm) – least count 1616 Example: Click to edit Master title style Certain digit -38 ml Uncertain digit -0.7/0.8/0.9 ml Least count -1 ml 1717  Click to edit and Precision Accuracy Master title style Precision – refers to the Accuracy – an indication closeness of two or of how close a set of more measurements to measurements is to the each other. exact (true) value. 1818 PClick to edit Master title Lowstyle accuracy Low accuracy r A Low precision High precision e c c c i u s r i a High accuracy High accuracy Low precision o c High precision n y 1919 Click to edit and Precision Accuracy Master title style Examples: TRUE VALUE: 12.5m a) 12.4m, 12.5m, 12.5m, 12.5m HA, HP b) 4.0m, 6.9m, 9.1m, 11.5m LA, LP c) 7.6m, 7.7m, 7.7m, 7.8m LA, HP d) 10.9m, 11.2m, 12.9m, 13.6m HA, LP 2020 Click to edit and Precision Accuracy Master title style PRECISION Precision is determined by a statistical method 𝛔 = standard deviation ∑ = summation called a standard 𝒙 = measurements/ exp. deviation. value ∑ 𝐱−𝐱 𝟐 𝒙 = mean 𝛔 = 𝑵= number of measurements 𝐍 2121 Click to edit and Precision Accuracy Master title style PRECISION Standard deviation is how much, on average, measurements differ from each other. High standard deviations indicate low precision, low standard deviations indicate high precision. 2222 Click to edit and Precision Accuracy Master title style ACCURACY experimental−accepted % error = x 100 accepted To determine if a value is accurate compare it to the accepted value. 2323 Click to edit and Precision Accuracy Master title style ACCURACY What percent error is acceptable? Notice that in order to determine the accuracy of a particular measurement, we have to know the ideal, true value. If the number of percent error increases the accuracy decreases. 2424 Click to edit and Precision Accuracy Master title style Example: Solve for the precision and accuracy of the given measurements below. TRUE VALUE: 6 kg x (x-x) (x−x) 2 A 5.90kg Range: 0 to 0.29 = High Precision B 6.05kg 0.3 to 0.99 = Low Precision C 6.05kg 1 and up = Not Precise D 6.15kg E 5.95kg 2525 Precision Click to edit and Accuracy Master title style Example: X (x-X) (x−X) 2 A 5.90kg -0.12kg 0.0144kg B 6.05kg 0.03kg 0.0009kg C 6.05kg 0.03kg 0.0009kg D 6.15kg 0.13kg 0.0169kg E 5.95kg -0.07kg 0.0049kg 2626 Click to edit Master title style NOTE: For PRECISION as well as for the ACCURACY, the range may vary depending on what measurements/ data are calculated. 2727 Precision andMaster Click to edit Accuracy title style Example: X (x-X) (x−X) 2 A 5.90kg -0.12kg 0.0144kg B 6.05kg 0.03kg 0.0009kg C 6.05kg 0.03kg 0.0009kg D 6.15kg 0.13kg 0.0169kg E 5.95kg -0.07kg 0.0049kg 2828 Click to edit Master title style NOTE: For ACCURACY, you may check the accuracy for each measurement (individually) or as a whole/ group (the mean value serves as the experimental value). 2929 Click to edit Master(next SEATWORK title style meeting) ☺ Coverage: Units and Measurements (Part 1 & 2) Note: Please Bring Your CALCULATOR all the time. DON’T ASK FOR PAPER, buy/ bring your own paper/ intermediate pad. 3030