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Mr. Klapholz Shaker Heights High School Physics and Measurement (1) Problem Solving How many Figures are Significant? • • • • • • • 12.3 800 801 8.00 x 102 800.0 0.007 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 801 8.00 x 102 800.0 0.007 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 {1 significant figure} 801 8.00 x 102 800.0 0.007 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 102 800.0 0.007 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 102 {3 significant figures} 800.0 0.007 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 102 {3 significant figures} 800.0 {4 significant figures} 0.007 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 102 {3 significant figures} 800.0 {4 significant figures} 0.007 {1 significant figure} 0.0070 How many Figures are Significant? • • • • • • • 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 102 {3 significant figures} 800.0 {4 significant figures} 0.007 {1 significant figure} 0.0070 {2 significant figures} Significant Figures after a Calculation • 12.3 + 4.567 + 0.8912 = ? • Without thinking about significant figures, the sum is 17.7582 • But we are confident only know about the 0.# decimal place, so the result is 17.8 • For addition or subtraction, keep your eye on which digits are significant. Significant Figures after a Calculation • 12.3 x 4.567 = ? • Without thinking about significant figures, the product is 56.1741 • But we are confident only of 3 significant digits, so the result is 56.2 • For multiplication and division, keep your eye on how many digits are significant. Propagation of Error Addition, Subtraction • If a string is so long that it takes two rulers to measure it, then its length could be 30.0 ± 0.1 cm PLUS 20.0 ± 0.1 cm. So the length is 50 ± ? cm. • For addition (or subtraction) just add the absolute errors. 0.1 cm + 0.1 cm = 0.2 cm. • So the string is 50 ± 0.2 cm long. Propagation of Errors (Multiplication and Division) • Speed = Distance ÷ Time. If you travel 90.0 ± 0.2 meters in 10.0 ± 0.3 seconds, then your speed = 9.00 ± ? m s-1. • For multiplication (or division) add the fractional errors and then use the result to find the error of the answer. • 0.2 / 90.0 = 0.0022 0.3 / 10.0 = 0.03 • 0.0022 + 0.03 = 0.032 • 0.032 x 9.00 = 0.29 • The speed is 9.00 ± 0.3 m s-1. Propagation of Errors (The ‘quick and dirty’ method that works for everything) • If A = 9.0 ± 0.2, and B = 1.4 ± 0.1, then AB = ? • AB ≈ 9.01.4 ≈ 21.7 ± ? • The greatest it could be is: 9.21.5 = 27.9 (that’s a difference of 6.2). • The least it could be is: 8.81.3 = 16.9 (that’s a difference of 3.8). • Average: (6.2 + 3.8) ÷ 2 = 5 • AB = 22 ± 5 Additional PPTs on Vectors are available under separate titles. Tonight’s HW: Go through the Physics and Measurement section in your textbook and scrutinize the “Example Questions” and solutions. Bring in your questions to tomorrow’s class.