1. Significant Figures and Percent Error

2. Rules for Significant Figures
Nonzero numbers are ALWAYS significant.
1287 g
78,483 cm
58 mL
638 mol
= 4 Sig Figs
= 5 Sig Figs
= 2 Sig Figs
= 3 Sig Figs

3. Rules for Significant Figures
Zeros in-between nonzero numbers are ALL significant.
101 mol
20,375 cd
1001 J
908 s
= 3 Sig Figs
= 5 Sig Figs
= 4 Sig Figs
= 3 Sig Figs

4. Rules for Significant Figures
Zeros after nonzero numbers (trailing zeros) WITH A DECIMAL PRESENT are significant
6.0 mg Kg
80.0 m mL
= 2 Sig Figs
= 5 Sig Figs
= 3 Sig Figs
= 4 Sig Figs

5. Rules for Significant Figures
Zeros in front of nonzero digits (preceding zeros) are not significant. They are called place holders.
0.78 Kg cd
290 amp
300 s
= 2 Sig Figs
= 3 Sig Figs
= 2 Sig Figs
= 1 Sig Figs

6. Zeros that are significant.
= 3 Sig Figs
202 cm L kg cd
= 6 Sig Figs
= 4 Sig Figs
= 5 Sig Figs

7. Zeros that are NOT significant, PLACE HOLDERS.
= 1 Sig Figs
50 g m J
9000 L
= 2 Sig Figs
= 3 Sig Figs
= 1 Sig Figs

8. = 4 Sig Figs = 3 Sig Figs = 4 Sig Figs = 4 Sig Figs
Zeros that are significant (called Trailing) and zeros that are not significant (call Place Holder).
= 4 Sig Figs
80020 s kg Amp L
= 3 Sig Figs
= 4 Sig Figs
= 4 Sig Figs

9. Making Calculations with Significant Digits
Multiplying and Dividing
The final answer is rounded to have the same number of significant figures as the measurement with the least number of significant figures.
755 cm x 33 cm = 24915
92 m x 20 m = 1840
25000 cm2
2000 m2

10. 0.894 g / 2.0 g = g 40.0 x 3.8 = x 4589 = / 789 = / 75.0 = x = 2.02
0.45g
1.50
932000
13.0
1.25
2.0

11. Making Calculations with Significant Digits
Adding and Subtracting The final answer is rounded so that it has the same number of digits past the decimal as the measurement with the least number of digits past the decimal
120.60
89.001
6.3 +
215.9

12. 756.05
23.02
733.03 −
733.03
9.002
2.32
45.659
56.981 +
56.98

13. 45
32.5
12.5 − 13

14. |Approximate Value − Exact Value|
PERCENT ERROR
  |Approximate Value − Exact Value|  
× 100%
|Exact Value|
Step 1: Calculate the error (subtract one value form the other) ignore any minus sign.
Step 2: Divide the error by the exact value (you will get a decimal number)
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

16. GOOD MORNING!!  PICK UP: Calculator GET OUT: Notebook, pencil,
TURN IN: Pennies if you brought them!! ‘
WARM UP:
1. How many significant figures are in these numbers? a b c d
e. 84
2. In your own words, what is the definition of accuracy and precision?
3. In the lab, Sandy and Danny produced 8.5 grams of their product. According to their calculations, they should have produced 9.5 grams. What was their percent error? (about 10%)