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AP Physics significant figures

Introduction to the significant figures

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AP Physics significant figures

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  1. I can . . . • applyaddition,subtraction,multiplication, and division to • numbers that have been measured. • determinethe correct location to round the answer to.

  2. + = 3 marbles 4 marbles 7 marbles Addition and Subtraction have always been done with COUNTED numbers.i.e. EXACT values

  3. Multiplication and Division have always been done with COUNTED numbers.i.e. EXACT values 7 x 4 = 28 squares 7 squares 4 squares

  4. 15 Apples ÷ 3 baskets = 5 apples per basket http://www.boreas-online.com/catalog/pics/Green_Apple.jpg http://www.eurocosm.com/Application/images/wicker-baskets/garden-vegetable-basket-lg.jpg

  5. We now need to learn how toaddand subtract,multiply and divideMEASURED numbers. i.e. Numbers with ERROR The rules ARE different!

  6. Thirty-five years ago,I learned that the dinosaurswent extinct 65,000,000 years ago http://baixaki.ig.com.br/site/w214.htm 65,000,000 years+ 35 years = 65,000,035 years

  7. 13,800,000,000 ± 100,000,000 years old

  8. We are 93,000,000 miles from the sun!(491,040,000,000 feet) = 491,040,000,000 – 10= 491,039,999,990 http://www.wizards.de/~frank/astro/

  9. 0.781 m 0.36 m 1 0 0 1 Area = Base x Height 0.36 m x 0.781 m = 0.28116 m2 ± .01 ± .001 ± .00001

  10. Multiplyingand Dividing Measured Numbers

  11. SignificantFigures“Sig Figs”

  12. Certain Guess ± .01 2.47 All three numbers are important. There are three “Significant Figures”. 0 1 2 3 4

  13. 8 millimeters 2.47 kilometers 1 sig figs 3 sig figs 2,470 meters .008 meters 3 sig figs 1 sig fig .000008 kilometers 2,470,000 millimeters 1 sig fig 3 sig figs Zeros are NOT “significant figures” when they are merely place holders.

  14. 1 0 1 0 1 0 0.7 ± .1 1 sig fig 0.67 ± .01 2 sig figs 0.675 ± .001 3 sig figs

  15. 1 0 1 0 1 0 0.4 ± .1 1 sig fig Zeros ARE significant when they make the measurement more precise! 0.40 ± .01 2 sig figs 0.400 ± .001 3 sig figs

  16. Zeros ARE significant when they are “sandwiched” 2.06 ± .01 3 sig figs 0 1 2 3 4 http://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Oreo.jpg/800px-Oreo.jpg

  17. Identify the Number that is a Guess Count the number of “Sig Figs” 23,560,0006,7002,004,6000.000182.006004594.000 82,000,0204,0003,004,600.002005,000.0.000,000,0451,001

  18. Rule formultiplying and dividingMEASURED numbers A chain is only as strongas its weakest link!

  19. Rule formultiplying and dividingMEASURED numbers = 400 Round your answer to thesamenumber of SIG FIGSas the LEASTnumber of SIG FIGS. 11 x 40 = 440 1 Sig Fig 2 Sig Figs 1 Sig Fig

  20. 0.781 m 0.36 m 1 0 0 1 Area = Base x Height 0.36 m x 0.781 m = 0.28116 m2 = 0.28 m2 3 Sig Figs 2 Sig Figs 2 Sig Figs Round your answer to thesamenumber of SIG FIGSas the LEASTnumber of SIG FIGS.

  21. Distance Time ÷ 2(145) cm.008 s = = 36,250 cm/s = 811.0627719 mi/hr = 800 mi/hr

  22. Rule formultiplying and dividingMEASURED numbers = 3.6 Round your answer to thesamenumber of SIG FIGSas the LEASTnumber of SIG FIGS. 1200 ÷ 335 = 3.582089… 2 Sig Figs 3 Sig Figs 2 Sig Figs

  23. Round to the correct number of sig figs. 3.456 x 95 = 328.32 = 330

  24. Addingand Subtracting Measured Numbers

  25. 2.5 ± .1 2.6 ± .1 2.5 ± .1 Accuracy Precision 2.5 ± .3 2.3 ± .3

  26. Degree ofPrecision The position of the guess. .03 45,000 Hundredths position Thousands position

  27. 1 0 1 0 Degree of Precision Which number is more precise? .7 .70

  28. Degree of Precision Which number is more precise? 8,280 8,000 7,000 9,000 8,000 7,000 9,000 8,000

  29. 4.25 in 6.25 in 2.00 in = + however, = + 6 in 4.25 in 6.25 in 2 in

  30. Identify the Number that is a Guess Find the DEGREE OF PRECISION 23,560,0006,7002,004,6000.000182.006004594.000 82,000,0204,0003,004,600.002005,000.0.000,000,0451,001 10,000’s 100’s 100’s 1,000,000th 10,000,000th 1,000th

  31. Rule foraddingand subtractingMEASURED numbers A chain is only as strongas its weakest link!

  32. Rule foradding and subtractingMEASURED numbers = .1 Round your answer to thesame DEGREE of PRECISIONas the LEASTPRECISE number. 4.3 - 4.187 = .113 Least precise

  33. Rule foraddingand subtractingMEASURED numbers = 14,100 Round your answer to thesame DEGREE of PRECISIONas the LEAST PRECISE number. 7,600 + 6,489 = 14,089 Least precise

  34. Round to the correct degree of precision. 3.426 + 9.5 = 12.926 = 12.9

  35. ∞ sig figs Counted numbers are considered to be EXACT i.e. an infinite number of sig figs. Example: Ninetypencils, each one is 12.9 grams. 90 x 12.9 = 1,161 grams total mass 3 sig figs = 1,160 grams total mass 3 sig figs

  36. Conversions WITHIN a measurement system are considered to be EXACT i.e. an infinite number of sig figs. Exactly 12 inches in 1 foot. Exactly 3 ft in 1 yard. Exactly 5280 ft in 1 mile. Exactly 100 centimeters in 1 meter. Exactly 1,000 meters in 1 kilometer. Exactly?2.54 centimeters in 1 inch. July 1, 1959 New standard Approximately1.6 kilometers in 1 mile.

  37. Conversions WITHIN a measurement system are considered to be EXACT i.e. an infinite number of sig figs. = 25,900 in ∞ sig figs How many inches is 2,160 ft? 2,160 x 12 = 25,920 in 3 sig figs 3 sig figs

  38. Using Scientific Notation to Properly Show Sig Figs. 256 x 39.0625 = 10,000 6 sig figs 3 sig figs = 1.00 x 104 3 sig figs

  39. TWO RULES 1) Addition and SubtractionIDENTIFYDEGREE OF PRECISION 2) Multiplication and DivisionCOUNTSIGNIFICANT FIGURES

  40. I can . . . • applyaddition,subtraction,multiplication, and division to • numbers that have been measured. • determinethe correct location to round the answer to.

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