1. Significant Figures!

2. There is uncertainty in all measurements.
The “certain” digits include all numbers read directly off of the measuring device PLUS one extra estimated digit.
Ex: This device is a graduated cylinder. The units are mL. The proper reading should be: 56.0mL (estimated digit)

3. The amount of definite digits depends on the measuring device.
An exact number has no uncertainty, and therefore has an infinite number of sig. figs.
Example: There are 25 people in this room, ….
Defined quantities are considered to be exact.
Ex: 12 in=1ft, 100cm=1m

4. Rules for Sig Figs!! All non-zero digits are significant
Example: sig. fig.
– 5 sig. fig.

5. 2. Leading zeros are never significant
Example: sig. fig.
0.04 – 1 sig. fig.

6. 3. Trapped zeros are always significant
Example: 205 – 3 sig. fig.
2005 – 4 sig. fig.

7. 4. Trailing zeros are sometimes significant
a) They are significant if the number contains a decimal point AND there is a nonzero number before the zero
Example: – 4 sig. fig.
0.450 – 3 sig. fig.

8. 4. Trailing zeros (cont.)
b) They are not sig. if the number does not contain a decimal point even if there are nonzero numbers before it
Example: 1550 – 3 sig. fig.
45000 – 2 sig. fig.

9. (Sig. if there is a decimal)
Summary
Never sig.
Always sig.
Sometimes sig.
(Sig. if there is a decimal)

10. Practice makes perfect!
How many sig figs are in the following?
4.59
3.00
20,020
0.0050
43,000
1.09 x 104 3 3 4 2 2 3

11. Sig Figs in Calculations
Addition and Subtraction:
LOOK at the decimal places!
The answer is rounded to the same number of decimal places as the number used in the calculation with the least decimal places.
Ex:
–7.12
7.81~ ~
4.23
7.8

12. Multiplication and Division: LOOK at the total number of sig figs
Multiplication and Division: LOOK at the total number of sig figs! The answer is rounded to the same number of sig. figs. as the number used in the calculation with the least significant figures Ex: 17.85/2.13= x ~ ~
0.0017
8.38