2. IV. Significant figures

3. Recall from yesterday…
Significant Digits(figures) – includes all of the digits that are known + a last digit that is estimated

4. A. Significant Figures
Measurements must always be reported to correct # of sig. figs.
Calculated answers depend on the # of sig figs in the values used in the original measurements.

5. B. Exact vs. Inexact Numbers
Exact numbers – numbers known exactly (by definition or by counting)
Ex: one dozen (12), one foot (12 inches), 1 teacher in the room
Have INFINITE significant figures
Inexact numbers – values with some uncertainty; anything measured using a piece of equipment (balance, graduated cylinder, beaker, etc.)
Ex: mass of penny = 3.03 grams

6. C. Precision vs. Accuracy
Precision – how closely individual measurements agree (repeatability)
Accuracy – how closely individual measurements agree with the correct or “true” value (bull’s-eye)
GREATER ACCURACY of an instrument means more SIGNIFICANT FIGURES.

7. D. Significant Figure Rules
RULE 1: all NONZERO numbers are significant
Examples:
96 g = 2 sig figs
61.4 cm = 3 sig figs
0.52 mL = 2 sig figs

8. D. Rules Continued Pacific Atlantic
If the decimal is present, start at the Pacific
If the decimal is absent, start from the Atlantic
Find the first # that is not a zero and the rest are significant

9. For Example… 0.00456 cm 1.000008 dL 1345 mL 10450 mm 1345000 km
dag dL
10450 mm hg Mm

10. You Try! How many sig figs in the following: Examples:
a) 1001 km
b) m
c) 129,870 m
d) km
e) 1.003
f) g
g) 20,000 cm
h) g
Number of Significant Figures:
a) 4
b) 4
c) 5
d) 1
e) 4
f) 5
g) 1
h) 2

11. E. Rounding Rules
When the rounding number is greater than or equal to 5: round up.
Ex: = 5.8
4.89 = 4.9
When the rounding number is less than 5: round down.
Ex: = 5.2
4.12 = 4.1

12. F. Multiplying & Dividing With Sig Figs
Rule: when multiplying or dividing measurements, round final answer to the smallest # of significant figures in the original measurements.

13. CALCULATIONS WITH SIG FIGS
Examples:
cm x cm = cm²
= 73.1 cm²
2. (1.13 m)( m) = m²
= 5.79 m²
cm² / cm = cm
= cm

14. G. Adding & Subtracting Sig Figs
Rule: When adding or subtracting, round the answer to the same number of decimal places as the measurement with the smallest number of decimal places.

15. CALCULATIONS WITH SIG FIGS
Examples: 1) cm 2) g 3) cm cm g cm cm g cm cm g = cm
= g
= 8.12 cm

16. Practice Addition Multiplication 165.5 cm + 8 cm + 4.37 cm =
2.6 cm x 3.78 cm = cm
= 178 cm
9.828 cm2
= 9.8 cm2