1 / 54

Significant Figures

Significant figures are crucial in scientific measurements, as they communicate the precision of values. This guide outlines which numbers are significant, including nonzero digits, certain zeros, and rules for addition, subtraction, multiplication, and division. It explains the importance of rounding and provides clear examples for applying the rules correctly. Whether you’re dealing with decimals or scientific notation, mastering significant figures ensures that your calculations reflect the true accuracy of your data.

maalik
Télécharger la présentation

Significant Figures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Significant Figures What is so significant about numbers??

  2. Just which numbers are significant? • All nonzero numbers (all numbers 1-9) – • 289 • 573 • 119

  3. Just which numbers are significant? • All nonzero numbers (all numbers 1-9) - 289 • All zeros b/w numbers – 909 • 501 • 3002 • 4000001

  4. Just which numbers are significant? • All nonzero numbers (all numbers 1-9) - 289 • All zeros b/w numbers – 909 • Zeros to the right of a number AND to the left of a written decimal point – • 250. • 700. • 10.

  5. Just which numbers are significant? • All nonzero numbers (all numbers 1-9) - 289 • All zeros b/w numbers – 909 • Zeros to the right of a number AND to the left of a written decimal point – 250. 700. 10. • Zeros to the right of a number AND to the right or a written decimal point – • 5.0 • 236.70 • 3.0 x 108

  6. These are NEVER significant • Zeros to the left of the decimal in numbers less than one • 0.8 • 0.222 *** these are placeholders only

  7. These are NEVER significant • Zeros to the left of the decimal in numbers less than one • Zeros to the right of a decimal, but to the left of the first number • 0.008 • 0.02

  8. Exceptions to the rule • Conversion factors – unlimited sig. fig. • 1 km/1000 m • 60 min/1 hr • 100 cm/1 m

  9. Exceptions to the rule • Conversion factors – unlimited sig. fig. • Counting numbers • 30 days • 12 in one dozen

  10. Calculations with sig. figs. • The following rules must be followed so that results reflect sig. figs. from your measurements taken originally…

  11. Addition & subtraction with sig. figs. • Your answer can’t be MORE precise than your LEAST precise measurement (what in the world does that mean??)

  12. Addition & subtraction with sig. figs. • Your answer can’t be MORE precise than your LEAST precise measurement • Your answer must be rounded to the same number of decimal places from the original problem… • 34.2 + 2.002 = ?

  13. Addition & subtraction • 34.2 + 2.002 = • Actual answer would be 36.202

  14. Addition & subtraction • Actual answer would be 36.202 • The least precise number is 34.2, therefore your answer MUST be to one decimal place

  15. Addition & subtraction • Actual answer would be 36.202 • The least precise number is 34.2, therefore your answer MUST be to one decimal place • Correct answer = 36.2

  16. Addition & subtraction • Example #2 • 3.999 – 1.77 = ?

  17. Addition & subtraction • 3.999 – 1.77 = • Actual answer would be 2.229

  18. Addition & subtraction • Actual answer would be 2.229 • The least precise number is 1.77, therefore your answer MUST be to two decimal places

  19. Addition & subtraction • Actual answer would be 2.229 • The least precise number is 1.77, therefore your answer MUST be to two decimal places • The correct answer would be 2.23

  20. Multiplication & division • Answer must be in the fewest number of sig. figs. from the original problem. • Example: • 45.6 x 1.009 = ?

  21. Multiplication & division • Answer must be in the fewest number of sig. figs. from the original problem. • Example: • 45.6 x 1.009 = ? • Actual is 46.0104

  22. Multiplication & division • Answer must be in the fewest number of sig. figs. from the original problem. • Example: • 45.6 x 1.009 = ? • Actual is 46.0104 • Smallest # of sig figs is 3… so answer must be in 3 sig figs.

  23. Multiplication & division • Answer must be in the fewest number of sig. figs. from the original problem. • Example: • 45.6 x 1.009 = ? • Actual is 46.0104 • Smallest # of sig figs is 3… so answer must be in 3 sig figs. • Correct answer is 46.0 (not just 46)

  24. Multiplication & division • Example #2 • 505 / 7 = ?

  25. Multiplication & division • Example #2 • 505 / 7 = ? • Actual answer is 72.14285714

  26. Multiplication & division • Example #2 • 505 / 7 = ? • Actual answer is 72.14285714 • Least number of sig figs is 1, so answer can only have one sig fig.

  27. Multiplication & division • Example #2 • 505 / 7 = ? • Actual answer is 72.14285714 • Least number of sig figs is 1, so answer can only have on sig fig. • Correct answer is 70 or it could be 7 x 101

  28. Rounding… • If the number right past the one you want to keep is: • Greater than 5  go up by one • 295.46 to 4 sig figs would be 295.5 • 999.97 to four sig figs would be 1000.

  29. Rounding… • If the number right past the one you want to keep is: • Greater than 5  go up by one • Less than 5  no change • 999.94 to four sig figs would be 999.9 • 564.44 to three sig figs would be 564

  30. Rounding… • If the number right past the one you want to keep is: • Greater than 5  go up by one • Less than 5  no change • 5 followed by a number  go up by one • 2.352 to two sig figs would be 2.4 • 4.156 to two sig figs would be 4.2

  31. Rounding… • If the number right past the one you want to keep is: • Greater than 5  go up by one • Less than 5  no change • 5 followed by a number  go up by one • 5 followed by nothing… look at the number before it… if it is ODD  go up by one • 3.375 to three sig figs would be 3.38 • 0.035 to one sig fig would be 0.04

  32. Rounding… • If the number right past the one you want to keep is: • Greater than 5  go up by one • Less than 5  no change • 5 followed by a number  go up by one • 5 followed by nothing… look at the number before it… if it is ODD  go up by one • 5 followed by nothing… look at the number before it… if it is EVEN  no change • 4.8785 to four sig figs would be 4.878 • 399.345 to five sig figs would be 399.34

  33. Scientific notation • Very large or very small numbers are expressed in scientific notation

  34. Scientific notation • Very large or very small numbers are expressed in scientific notation • M x 10n

  35. Scientific notation • Very large or very small numbers are expressed in scientific notation • M x 10n • “M” must be 1 or greater, but less than 10 • 2.2 x 105

  36. Scientific notation • Very large or very small numbers are expressed in scientific notation • M x 10n • “M” must be 1 or greater, but less than 10 • All numbers that represent “M” are significant • 3.10 x 109 • 9.98 x 103

  37. Scientific notation • Very large or very small numbers are expressed in scientific notation • M x 10n • “M” must be 1 or greater, but less than 10 • All numbers that represent “M” are significant • Numbers that represent “n” are whole numbers, positive or negative • 6.022 x 1023 • 2.1 x 10-5

  38. Scientific notation • Very large or very small numbers are expressed in scientific notation • M x 10n • “M” must be 1 or greater, but less than 10 • All numbers that represent “M” are significant • Numbers that represent “n” are whole numbers, positive or negative • Examples: • 270,000 would be 2.7 x 105 • The understood decimal is behind the last zero…move the decimal until it makes the number represent “M” • 0.000000505 would be 5.05 x 10-7

  39. Calculations w/ scientific notation • Addition and subtraction: • All numbers must have the same exponent before “M” can be added or subtracted • Answer will have the same exponent value as originals • Don’t forget rules w/ sig figs… they still apply!! • 2.4 x 102 + 5.7 x 102 = 8.1 x 102 • 9.05 x 105 – 5.5 x 105 = actual 3.55 x 105 • Correct is 3.6 x 105

  40. Calculations w/ scientific notation • Addition and subtraction: • All numbers must have the same exponent before “M” can be added or subtracted • The problem comes when exponents are DIFFERENT…  • You must MAKE the exponents the same… • LL / RR = left larger or right reduce  when you move the decimal it changes the exponent -- ALWAYS

  41. Calculations w/ scientific notation • Addition and subtraction: • 2.5 x 104 + 5.2 x 103 = • Choose which number you want to deal with… either will work out

  42. Calculations w/ scientific notation • Addition and subtraction: • 2.5 x 104 + 5.2 x 103 = • Choose which number you want to deal with… either will work out • I like to change the smaller exponent to the larger  5.2 x 103

  43. Calculations w/ scientific notation • Addition and subtraction: • 2.5 x 104 + 5.2 x 103 = • Choose which number you want to deal with… either will work out • I like to change the smaller exponent to the larger  5.2 x 103 • I want to make the exp. larger, so I move the decimal one place to the left

  44. Calculations w/ scientific notation • Addition and subtraction: • 2.5 x 104 + 5.2 x 103 = • Choose which number you want to deal with… either will work out • I like to change the smaller exponent to the larger  5.2 x 103 • I want to make the exp. larger, so I move the decimal one place to the left • This makes it .52 x 104

  45. Calculations w/ scientific notation • Addition and subtraction: • 2.5 x 104 + 5.2 x 103 = • Choose which number you want to deal with… either will work out • I like to change the smaller exponent to the larger  5.2 x 103 • I want to make the exp. larger, so I move the decimal one place to the left • This makes it .52 x 104 • Now “M” can be added because exp are the same • Actual answer = 3.02 x 104 • Correct answer = 3.0 x 104

  46. Calculations w/ scientific notation • Multiplication – this one is much easier  • 3.0 x 103 x 4.0 x 104

  47. Calculations w/ scientific notation • Multiplication – this one is much easier  • 3.0 x 103 x 4.0 x 104 • You will multiply your “M”s together (12)

  48. Calculations w/ scientific notation • Multiplication – this one is much easier  • 3.0 x 103 x 4.0 x 104 • You will multiply your “M”s together (12) • Then add your “n”s together (7)

  49. Calculations w/ scientific notation • Multiplication – this one is much easier  • 3.0 x 103 x 4.0 x 104 • You will multiply your “M”s together (12) • Then add your “n”s together (7) • CAREFUL… you will often need to move the decimal to keep correct scientific notation

  50. Calculations w/ scientific notation • Multiplication – this one is much easier  • 3.0 x 103 x 4.0 x 104 • You will multiply your “M”s together (12) • Then add your “n”s together (7) • CAREFUL… you will often need to move the decimal to keep correct scientific notation • Actual answer would be 12 x 107

More Related