Chemistry
Significant Figures Notes
Objectives: 1) You will be expected to count
the number of significant figures in a measurement.
2) You will be expected to write
the final answer of a calculation involving addition/subtraction/multiplication/division with the appropriate number of significant figures.
Accuracy v. Precision A measurement can be
precise and have a small random error. And, a measurement can be accurate and have a small systematic
error. Note below whether each of the darts represent
being precise (P) and/or accurate (A).
Significant Figures in Numbers Significant figures indicate the precision of a measurement or final
answer. This is the simplest method that scientists
have for reporting random error. The format for significant figures is to write all of the certain digits followed
by one uncertain digit. Thus when making measurements write the measurement one digit beyond what
the markings indicate. The simplest way to confirm
significant figures is to rewrite the number in scientific
notation. The number of digits in the significand are
the number of significant figures. The rules for determining the number of significant figures are:
Example 1 How many significant figures are in
the following measurement: 0.8801 g.
Example 2 How many significant figures are in
the following measurement: 0.0200 m.
1.
How many significant figures are in the following
measurement: 300 kg.
2.
How many significant figures are in the following
measurement: 32.1 s.
Example 3 33.01 g − 0.1327 g
3
3
.
0
1
0
.
1
3
2
7
3
2
.
8
7
7
3
We then round to the nearest hundreth, because it
is the last digit before the dashed line. The answer
is then: 32.88 g.
Example 4 200.11 cm · 3 cm
Note that 3 cm has 1 significant figure, while
200.11 cm has 5 significant figures. Thus, you multiply the two numbers and the final answer also
should have 1 significant figure.
200.11 · 3 = 600.33, but our answer would be
600 cm.
3.
63.11 g − 1.232 g
4.
12.5 m · 3.612 m
1. Non-zero digits are always significant.
2. Any zeros between significant digits are significant.
3. A final zero or trailing zeros in the decimal portion only are significant.
4. Zeros to the right of non-zero digits are not significant, unless the number includes a decimal
point.
The rules for propagating significant figures are:
Addition/Subtraction Add/subtract as normally
and round to the least number of places
in the decimal portion of any number being
added/subtracted.
Multiplication/Division The number with the
least number of significant figures determines the
number of significant figures of the final answer.
Terry HS
Chemistry
5.
65.4 m
3.1 s
6.
12.04×1023 C atoms
24 g C
Page 2 of 2
Significant Figures in Measurements For rulers,
graduated cylinders, graduated pipettes, and burets
always read one digit beyond what is marked. For
volumetric flasks and pipettes measure to the calibration line for that size. These can be designed to other
contain OR deliver a volume.
Buret readings: Always measure from the bottom
of the meniscus and note that our 50 mL burets start
with 0.00 mL at the top and 50.00 mL at the bottom.
Here are some densities of common substances. What
do you notice?