Significant Figures sig figs l Rules l All

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

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

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

Practice Makes Perfect! l l l How many sig figs? PRESENT Start from LEFT and count all #’s from first nonzero 4. 001 ü 0. 0203 ü 100. ü 4 3 3 l l ABSENT Start from RIGHT and count all #’s from first nonzero 4001 ü 503000 ü 100 ü 4 3 1

Sig. Figs in Scientific Notation l All #’s (excluding x 10 xx) ARE significant How many sig. figs? : Ø 3. 2 x 103 Ø 3. 20 x 103 l Ø Put 0. 08400 in scientific notation w/ sig. figs

Sig. Fig. Calculations Multiplication/Division Rules: l The measurement w/ the smallest # of sig. figs determines the # of sig. figs in answer l Let’s Practice!!! l 6. 221 cm x 5. 2 cm = 32. 3492 cm 2 4 2 ü How many sig figs in final answer? ? ? ü And the answer is…. 32 cm 2 l

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

For example 27. 93 + 6. 4 l + First line up the decimal places Then do the adding 27. 93 Find the estimated 6. 4 numbers in the problem 34. 33 This answer must be rounded to the tenths place

Rounding rules l l l 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

I. Significant Figures How many significant figures does each of the following numbers contain. 7 6 2. 9, 999. 900 ______ 2 4. 4. 7 x 10 -3 ______ 2 6. 84. 007 ______ 1. 6. 03001 ______ 3. 0. 00092 ______ 5. 9. 1 x 108 ______ 4 7. 3. 206 ______ 9. 4. 20 ______ 3 8. 3. 8 x 10 -5 10. 42, 300 2 5 2 3 ____________

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 = ___________