Download Significant Figures!!!!!!!

Significant Figures!
• 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)
• 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,
25.0000000000000000000….
• Defined quantities are considered to be exact.
Ex: 12 in=1ft, 100cm=1m
Rules for Sig Figs!!
1. All non-zero digits are significant
Example: 2.17 - 3 sig. fig.
3894.6 – 5 sig. fig.
2. Leading zeros are never significant
Example:
0.003 - 1 sig. fig.
0.04 – 1 sig. fig.
3. Trapped zeros are always significant
Example:
205 – 3 sig. fig.
2005 – 4 sig. fig.
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: 155.0 – 4 sig. fig.
0.450 – 3 sig. fig.
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.
Summary
0.000424000600
Never sig.
Always sig.
Sometimes sig.
(Sig. if there is
a decimal)
Practice makes perfect!
How many sig figs are in the following?
1. 4.59 3
2. 3.00 3
3. 20,020 4
4. 0.0050 2
5. 43,000 2
6. 1.09 x 104 3
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: 5.7
11.345
+ 2.11
–7.12
7.81~ 7.8
4.225 ~ 4.23
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
0.0561
Ex: 17.85/2.13=
x 0.030
8.38028~ 8.38
0.001683~ 0.0017