Significant Figures (sig. figs)

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 LEFT Start from RIGHT
• count all s from count all s from
• first nonzero first nonzero

4
Practice Makes Perfect!

• ABSENT
• Start from RIGHT and count all s from first
  nonzero
• 4001
• 503000
• 100

• How many sig figs?
• PRESENT
• Start from LEFT and count all s from first
  nonzero
• 4.001
• 0.0203
• 100.

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
• Lets 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
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 youre
  rounding.
• If it is 0 to 4 dont 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

• 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
2
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 ______________________