Physics (significant figures)

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Physics (significant figures)

  1. 1. THE NUMERICAL SIDE OF PHYSICS
  2. 2. Objectives <ul><li>Determine the number of significant figures in a numerical value. </li></ul><ul><li>Convert a number from normal notation to scientific notation </li></ul><ul><li>Use unit analysis to convert a measurement to another set of units </li></ul>
  3. 3. Significant Figures <ul><li>the number of meaningful digits in a measured or calculated quantity </li></ul>
  4. 4. Guidelines for Using Significant Figures
  5. 5. <ul><li>Any digit that is not zero </li></ul><ul><li>is significant </li></ul><ul><li>Example: 845 cm has 3 SFs </li></ul>
  6. 6. <ul><li>Zeros between nonzero digits </li></ul><ul><li>are significant </li></ul><ul><li>Example: 40,501 kg contains 5 SFs </li></ul>
  7. 7. <ul><li>Zeros to the left of the first </li></ul><ul><li>nonzero digit are </li></ul><ul><li>not significant </li></ul><ul><li>Example: 0.008 L contains 1 SF </li></ul>
  8. 8. <ul><li>If the number is >1, then all </li></ul><ul><li>the zeros written to the right </li></ul><ul><li>of the decimal point is </li></ul><ul><li>significant </li></ul><ul><li>Example: 2.00 mg has 3 SFs </li></ul>
  9. 9. <ul><li>If a number is <1, the zeros </li></ul><ul><li>that are at the end of the </li></ul><ul><li>number and the zeros that are </li></ul><ul><li>between nonzero digits are </li></ul><ul><li>significant </li></ul><ul><li>Examples: 0.090 kg has 2 SFs </li></ul><ul><li>0.0405 g has 3 SFs </li></ul>
  10. 10. <ul><li>For numbers that do not contain </li></ul><ul><li>decimal points, the trailing zeros </li></ul><ul><li>(that is, zeros after the last </li></ul><ul><li>nonzero digit) may or may not </li></ul><ul><li>be significant </li></ul><ul><li>Example: 400 can be expressed as </li></ul><ul><li>4 x 10 2 for 1 SF </li></ul><ul><li>4.0 x 10 2 for 2 SFs </li></ul>
  11. 11. Rounding Off <ul><li>A number is rounded off to the </li></ul><ul><li>desired number of significant </li></ul><ul><li>figures by dropping one or more </li></ul><ul><li>digits to the right </li></ul>
  12. 12. Rounding Off Rules
  13. 13. <ul><li>When the first digit dropped </li></ul><ul><li>is <5, the last digit retained </li></ul><ul><li>should remain unchanged </li></ul><ul><li>Example: </li></ul><ul><li>4.13 can be rounded off to 4.1 </li></ul>
  14. 14. <ul><li>When it is >5, 1 is added to the </li></ul><ul><li>last digit retained </li></ul><ul><li>Example: </li></ul><ul><li>4.17 can be rounded off to 4.2 </li></ul>
  15. 15. <ul><li>When it is exactly 5, 1 is added </li></ul><ul><li>to the last digit retained if </li></ul><ul><li>that digit is odd, </li></ul><ul><li>but remains as is when </li></ul><ul><li>it is even </li></ul><ul><li>Examples: 4.15 can be rounded off to 4.2 </li></ul><ul><li>4.45 can be rounded off to 4.4 </li></ul>
  16. 16. <ul><li>In chain calculations, only </li></ul><ul><li>the final answer is rounded </li></ul><ul><li>off to the correct number of </li></ul><ul><li>significant figures </li></ul>
  17. 17. Addition and Subtraction
  18. 18. <ul><li>In addition and subtraction, </li></ul><ul><li>the answer cannot have more </li></ul><ul><li>digits to the right of the </li></ul><ul><li>decimal point than either of the </li></ul><ul><li>original numbers </li></ul>
  19. 19. Example <ul><li> 89.332 </li></ul><ul><li>+ 1.1 </li></ul><ul><li>90.432 </li></ul> one digit after the decimal pt.  round off to 90.4
  20. 20. Multiplication and Division
  21. 21. <ul><li>In multiplication and division, </li></ul><ul><li>the number of significant figures </li></ul><ul><li>in the final product or quotient is </li></ul><ul><li>determined by the original </li></ul><ul><li>number that has the smallest </li></ul><ul><li>number of significant figures </li></ul>
  22. 22. Examples: <ul><li>2.8 x 4.5039 = </li></ul><ul><li>12.61092  round off to 13 </li></ul><ul><li>6.85/112.04 = </li></ul><ul><li>0.0611388789  round off to 0.0611 </li></ul>
  23. 23. Scientific Notation <ul><li>used when working with very large and </li></ul><ul><li>very small numbers </li></ul><ul><li>expressed in the form: </li></ul><ul><li>N x 10 n </li></ul><ul><li>where N- number between 1 and 10 </li></ul><ul><li>n- exponent, + or - integer </li></ul>
  24. 24. <ul><li>If the decimal point </li></ul><ul><li>has to be moved: </li></ul><ul><li>to the left n is + </li></ul><ul><li>to the right n is - </li></ul><ul><li>Examples: </li></ul><ul><li>568.762 = 5.68762 x 10 2 n = 2 </li></ul><ul><li>0.00000772 = 7.72 x 10 -6 n = - 6 </li></ul>
  25. 25. Addition and Subtraction
  26. 26. <ul><li>To add or subtract using scientific notation, write each quantity, say N 1 and N 2 -with the same exponent n then combine N 1 and N 2 the exponents remain the same </li></ul><ul><li>Example: </li></ul><ul><li>(7.4 x 10 3 ) + (2.1 x 10 3 ) = 9.5 x 10 3 </li></ul>
  27. 27. Multiplication and Division
  28. 28. <ul><li>To multiply numbers expressed in scientific notation, we multiply N 1 and N 2 and then add the exponents together </li></ul><ul><li>Example: </li></ul><ul><li>(8.0 x 10 4 ) x (5.0 x 10 2 ) </li></ul><ul><li>= (8.0 x 5.0)( 10 4+2 ) = 40 x 10 6 </li></ul><ul><li> = 4.0 x 10 7 </li></ul>
  29. 29. <ul><li>To divide using scientific </li></ul><ul><li>notation, we divide </li></ul><ul><li>N 1 and N 2 and then subtract </li></ul><ul><li>the exponents </li></ul><ul><li>Example: </li></ul><ul><li>(6.9 x 10 7 )/(3.0 x 10- 5 ) = (6.9/3.0) x 10 7-(-5) </li></ul><ul><li> = 2.3 x 10 12 </li></ul>
  30. 30. Unit Conversions
  31. 31. <ul><li>SI Base Units </li></ul>Base Quantity Name of Unit Symbol Length meter m Mass kilogram kg Time second s Electrical current ampere A Temperature kelvin K Amount of substance mole mol Luminous intensity candela cd
  32. 32. <ul><li>Prefixes used with SI Units </li></ul>Prefix Symbol Meaning Example Tera- T 10 12 1 terameter (Tm) = 1 x 10 12 m Giga- G 10 9 1 gigameter (Gm) = 1 x 10 9 m Mega- M 10 6 1 megameter (Mm) = 1 x 10 6 m Kilo- k 10 3 1 kilometer (km) = 1 x 10 3 m Deci- d 10 -1 1 decimeter (dm) = 0.1 m Centi- c 10 -2 1 centimeter (cm) = 0.01 m Milli- m 10 -3 1 millimeter (mm) = 0.001 m Micro- μ 10 -6 1 micrometer (μm) = 1 x 10 -6 m Nano- n 10 -9 1 nanometer (nm) = 1 x 10 -9 m Pico- p 10 -12 1 picometer (pm) = 1 x 10 -12 m
  33. 33. <ul><li>Unit Conversion Factors </li></ul>LENGTH 1 m = 100 cm = 1000 mm = 10 6 μm = 10 9 nm 1 km = 1000 m = 0.6214 mi 1 in = 2.540 cm 1 ft = 30.48 cm 1 yd = 91.44 cm
  34. 34. TIME 1 min = 60 s 1 h = 3600 s 1 d = 86,400 s 1 y = 365.24 d = 3.156 x 10 7 s
  35. 35. MASS 1 kg = 10 3 g = 2.205 lb
  36. 36. VOLUME 1 liter= 1000 mL = 1000 cm 3 = 1 dm 3 = 10 -3 m 3 1 ft 3 = 0.02832 m 3 = 28.32 liters = 7.477 gallons 1 gallon = 3.788 liters
  37. 37. Simple Conversion <ul><li>Convert 22 inches into feet </li></ul>
  38. 38. Answer <ul><li>22 in x (1 ft/12 in) = 1.8 ft </li></ul>
  39. 39. Multiple Conversion <ul><li>Convert 2,700 mL into gallon </li></ul>
  40. 40. Answer <ul><li>2700 mL x (1 L/1000 mL) x (1 gal/3.788 L) </li></ul><ul><li>= 0.7128 gal </li></ul>
  41. 41. Determine the number of SFs of the following measurements <ul><li>1. 478 cm 6. 0.043 kg </li></ul><ul><li>2. 6.01 g 7. 560 mg </li></ul><ul><li>3. 0.825 m 8. 453.2 cm </li></ul><ul><li>4. 3001 km 9. 2.60 dm </li></ul><ul><li>5. 1,020 mL 10. 200 L </li></ul>
  42. 42. Perform the operations and express the answers to the correct number of SFs <ul><li>1. 11,254.1 g + 0.1983 g </li></ul><ul><li>0.0154 kg / 88.3 mL </li></ul><ul><li>66.59 L – 3.113 L </li></ul><ul><li>2.64 x 103 cm + 3.27 x 102 cm </li></ul><ul><li>8.16 m x 5.1355 m </li></ul>
  43. 43. Express the ff. numbers in scientific notation <ul><ul><li>0.000000027 </li></ul></ul><ul><ul><li>0.096 </li></ul></ul><ul><ul><li>356 </li></ul></ul><ul><ul><li>602,200,000,000,000,000,000,000 </li></ul></ul><ul><ul><li>0.00000000000000000000000166 </li></ul></ul>
  44. 44. <ul><li>A person’s average daily intake of glucose (a form of sugar) is 0.0833 pound (lb). What is this mass in milligrams? </li></ul>
  45. 45. <ul><li>An average adult has 5.2 L of blood. What is the volume of blood in m 3 ? </li></ul>

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