Significant Figures (sig. figs)Significant Figures (sig. figs)

RulesRules::All All non-zero #’snon-zero #’s are significant are significant Some zeros are significant; others Some zeros are significant; others

are place holdersare place holders

Sig FigsSig Figs

Only measurements have sig figs.Only measurements have sig figs.Counted numbers are exactCounted numbers are exactA dozen is exactly 12A dozen is exactly 12A piece of paper is measured 11 A piece of paper is measured 11

inches tall.inches tall.Being able to locate, and count Being able to locate, and count

significant figures is an important significant figures is an important skill.skill.

Atlantic-Pacific RuleAtlantic-Pacific Rule

Ask yourselfAsk yourself: self, is there a decimal?: self, is there a decimal?

PPACIFICACIFIC AATLANTICTLANTIC

((PPresent)resent) ((AAbsent)bsent)

Start from Start from LEFTLEFT Start from Start from RIGHTRIGHT

& count & count all #’sall #’s from from & count & count all #’sall #’s from from

first nonzero first nonzero first nonzerofirst nonzero

Practice Makes Perfect!Practice Makes Perfect!

How many sig figs?How many sig figs? PRESENTPRESENT Start fromStart from LEFTLEFT and count all and count all

#’s from first nonzero#’s from first nonzero

4.0014.001 0.0203 0.0203 100.100.

ABSENTABSENT Start from Start from RIGHTRIGHT and count and count

all #’s from first nonzeroall #’s from first nonzero

40014001 503000503000 100100

4

3

3

4

3

1

Sig. Figs in Scientific NotationSig. Figs in Scientific Notation

All #’sAll #’s (excluding x 10 (excluding x 10xxxx) ) AREARE significant significant

How many sig. figs?How many sig. figs?:: 3.2 x 103.2 x 1033 3.20 x 103.20 x 1033

Put 0.08400 in scientific notation w/ sig. figsPut 0.08400 in scientific notation w/ sig. figs

Sig. Fig. CalculationsSig. Fig. Calculations

Multiplication/DivisionMultiplication/Division Rules:Rules: The measurement w/ the The measurement w/ the smallestsmallest # of sig. figs # of sig. figs

determines the # of sig. figs in answerdetermines the # of sig. figs in answer

Let’s Practice!!!Let’s Practice!!! 6.221cm x 5.2cm = 32.3492 cm6.221cm x 5.2cm = 32.3492 cm22 4 4 2 2 How many sig figs in final answer???How many sig figs in final answer??? And the answer is….And the answer is…. 32 32 cmcm22

Adding and subtracting Adding and subtracting with sig figswith sig figs

The last sig fig in a measurement is The last sig fig in a measurement is an estimate.an estimate.

Your answer when you add or Your answer when you add or subtract can not be better than your subtract can not be better than your worst estimate. worst estimate.

have to round it to the least place of have to round it to the least place of the measurement in the problemthe measurement in the problem

For example

27.93 6.4+ First line up the decimal places

27.936.4+

Then do the addingFind the estimated numbers in the problem

27.936.4

This answer must be rounded to the tenths place

34.3334.33

Rounding rules Rounding rules

look at the number behind the one you’re look at the number behind the one you’re rounding.rounding.

If it is 0 to 4 don’t change itIf it is 0 to 4 don’t change it If it is 5 to 9 make it one biggerIf it is 5 to 9 make it one bigger round 45.462 to four sig figsround 45.462 to four sig figs to three sig figsto three sig figs to two sig figsto two sig figs to one sig fig to one sig fig

Significant FiguresSignificant FiguresI.I. How many significant figures does How many significant figures does each of the following numbers contain.each of the following numbers contain.

1. 6.03001 ____________1. 6.03001 ____________ 2. 9,999.900 ____________ 2. 9,999.900 ____________

3. 0.00092 ___________3. 0.00092 ___________ 4. 4.7 x 10 4. 4.7 x 10-3 -3 ____________ ____________

5. 9.1 x 105. 9.1 x 108 8 ___________ 6. 84.007 ____________ ___________ 6. 84.007 ____________

7. 3.2067. 3.206 ____________ 8. 3.8 x 10 ____________ 8. 3.8 x 10-5 -5 ________________________

9. 4.209. 4.20 ____________ 10. 42,300 ____________ ____________ 10. 42,300 ____________

  

  

  

6

2

2

4

3

2

2

5

3

7

II. II. Round off the following to three significant Round off the following to three significant figures.figures.

  11. 0.0102511. 0.01025 ________________________ 12. 0.0054312. 0.00543 ________________________

   13. 7.013 13. 7.013 ________________________ 15. 0.0342615. 0.03426 ________________________

  16. 234.7816. 234.78 ________________________ 17. 124,53017. 124,530 ________________________

  

III. III. Perform the following operations and express the result to 3 significant Perform the following operations and express the result to 3 significant figures.figures.

  18. 50.05 x 2042 = 18. 50.05 x 2042 = ____________________________________________

  19. 9150 / 6375 = 19. 9150 / 6375 = ____________________________________________

  20. 3.02 x 0.022 = 20. 3.02 x 0.022 = ____________________________________________

  21. 0.076 / 1.23 = 21. 0.076 / 1.23 = ____________________________________________

  22. 0.375 + 1.26 + 48.0 =22. 0.375 + 1.26 + 48.0 = ____________________________________________

  23. 8.5 - 0.62 + 0.7805 + 210.8 =23. 8.5 - 0.62 + 0.7805 + 210.8 = ____________________________________________

  24. 2972 - 0.262 + 246 + 2.46 =24. 2972 - 0.262 + 246 + 2.46 = ____________________________________________