math

1. Significant Figures (sig. figs)Significant Figures (sig. figs)
RulesRules::
AllAll non-zero #’snon-zero #’s are significantare significant
Some zeros are significant; others areSome zeros are significant; others are
place holdersplace holders

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

3. 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 fromStart from LEFTLEFT Start fromStart from RIGHTRIGHT
& count& count all #’sall #’s fromfrom & count& count all #’sall #’s fromfrom
first nonzerofirst nonzero first nonzerofirst nonzero

4. Practice Makes Perfect!Practice Makes Perfect!
 How many sig figs?How many sig figs?
 PRESENTPRESENT
 Start fromStart from LEFTLEFT and count all #’sand count all #’s
from first nonzerofrom first nonzero
 4.0014.001
 0.02030.0203
 100.100.
 ABSENTABSENT
 Start fromStart from RIGHTRIGHT and count alland count all
#’s from first nonzero#’s from first nonzero
 40014001
 503000503000
 100100
4
3
3
4
3
1

5. Sig. Figs in Scientific NotationSig. Figs in Scientific Notation
 All #’sAll #’s (excluding x 10(excluding x 10xxxx
)) AREARE significantsignificant
 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

6. Sig. Fig. CalculationsSig. Fig. Calculations
Multiplication/DivisionMultiplication/Division
 Rules:Rules:
 The measurement w/ theThe 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
44 22
 How many sig figs in final answer???How many sig figs in final answer???
 And the answer is….And the answer is…. 3232 cmcm22

7. Adding and subtracting with sigAdding and subtracting with sig
figsfigs
The last sig fig in a measurement is anThe last sig fig in a measurement is an
estimate.estimate.
Your answer when you add or subtractYour answer when you add or subtract
can not be better than your worstcan not be better than your worst
estimate.estimate.
have to round it to the least place of thehave to round it to the least place of the
measurement in the problemmeasurement in the problem

8. For example
27.93 6.4+
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
34.3334.33

9. Rounding rulesRounding rules
 look at the number behind the one you’relook 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 figto one sig fig

10. Significant FiguresSignificant Figures
I.I. How many significant figures does each ofHow many significant figures does each of
the following numbers contain.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 104. 4.7 x 10-3-3
________________________
5. 9.1 x 105. 9.1 x 1088
___________ 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

11. II.II. Round off the following to three significant figures.Round off the following to three significant figures.
11. 0.0102511. 0.01025 ________________________ 12. 0.0054312. 0.00543 ________________________
13. 7.01313. 7.013 ________________________ 15. 0.0342615. 0.03426 ________________________
16. 234.7816. 234.78 ________________________ 17. 124,53017. 124,530 ________________________

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