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Significant Figures (sig. figs)

Significant Figures (sig. figs). Rules : All non-zero #’s are significant Some zeros are significant; others are place holders. Sig Figs. Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12 A a piece of paper is measured 11 inches tall.

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Significant Figures (sig. figs)

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  1. Significant Figures (sig. figs) • Rules: • All non-zero #’s are significant • Some zeros are significant; others are place holders

  2. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • A a piece of paper is measured 11 inches tall. • Being able to locate, and count significant figures is an important skill.

  3. Atlantic-Pacific Rule • Ask yourself: self, is there a decimal? PACIFIC ATLANTIC (Present) (Absent) Start from LEFTStart from RIGHT & count all #’s from & count all #’s from first nonzero first nonzero

  4. How many sig figs? PRESENT Start fromLEFTand count all #’s from first nonzero 4.001 0.0203 100. ABSENT Start from RIGHTand count all #’s from first nonzero 4001 503000 100 Practice Makes Perfect! 4 4 3 3 3 1

  5. Sig. Figs in Scientific Notation • All #’s (excluding x 10xx) ARE significant • How many sig. figs?: • 3.2 x 103 • 3.20 x 103 • Put 0.08400 in scientific notation w/ sig. figs

  6. Sig. Fig. Calculations Multiplication/Division • Rules: • The measurement w/ the smallest# of sig. figs determines the # of sig. figs in answer • Let’s Practice!!! • 6.221cm x 5.2cm = 32.3492 cm2 4 2 • How many sig figs in final answer??? • And the answer is…. 32 cm2

  7. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate. • Your answer when you add or subtract can not be better than your worst estimate. • have to round it to the least place of the measurement in the problem

  8. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem 34.33 34.33 This answer must be rounded to the tenths place

  9. Rounding rules • look at the number behind the one you’re rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig

  10. Significant FiguresI. How many significant figures does each of the following numbers contain. 7 6 2 2 1. 6.03001 ____________ 2. 9,999.900 ____________ 3. 0.00092 ___________ 4. 4.7 x 10-3 ____________ 5. 9.1 x 108 ___________ 6. 84.007 ____________ 7. 3.206 ____________ 8. 3.8 x 10-5 ____________ 9. 4.20 ____________ 10. 42,300 ____________ 2 5 4 2 3 3

  11. II. Round off the following to three significant figures.11. 0.01025 ____________ 12. 0.00543 ____________ 13. 7.013 ____________ 15. 0.03426 ____________ 16. 234.78 ____________ 17. 124,530 ____________

  12. III. Perform the following operations and express the result to 3 significant figures. 18. 50.05 x 2042 = ______________________ 19. 9150 / 6375 = ______________________ 20. 3.02 x 0.022 = ______________________ 21. 0.076 / 1.23 = ______________________ 22. 0.375 + 1.26 + 48.0 = ______________________ 23. 8.5 - 0.62 + 0.7805 + 210.8 = ______________________ 24. 2972 - 0.262 + 246 + 2.46 = ______________________

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