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

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

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

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

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

Sig. Figs in Scientific Notation All All #’s #’s (excluding x 10 xx ) 10 xx ) ARE ARE significant How How many sig. figs?:  3.2  3.2 x 10 3  3.20  3.20 x 10 3  Put  Put 0.08400 in scientific notation w/ sig. figs

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

Adding and subtracting with sig figs The last sig fig in a measurement is an estimate. 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. 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 have to round it to the least place of the measurement in the problem

For example 27.936.4+ l First line up the decimal places 27.93 6.4+ Then do the adding Find the estimated numbers in the problem 27.93 6.4 This answer must be rounded to the tenths place 34.33

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

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

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____________ 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____________

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 =______________________ 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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