physics and measurement (1)
DESCRIPTION
Mr. Klapholz Shaker Heights High School. Physics and Measurement (1). Problem Solving. How many Figures are Significant?. 12.3 800 801 8.00 x 10 2 800.0 0.007 0.0070. How many Figures are Significant?. 12.3 {3 significant figures} 800 801 8.00 x 10 2 800.0 0.007 0.0070. - PowerPoint PPT PresentationTRANSCRIPT
Physics and Measurement (1)
Problem Solving
Mr. KlapholzShaker Heights
High School
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 ErrorAddition, 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.