Transcript Significant Figures

Chemistry Notes
Significant Figures &
Scientific Notation
Describing Numbers
 We can describe and use numbers in
several different ways. These include
scientific notation and significant
figures.
Scientific Notation
In scientific notation,
a number is written
as the product of
two numbers: a
coefficient and 10
raised to a power.
Examples:
Convert to or from Scientific
Notation:
241
6015
0.0162
0.512
6.62 x 102
3.4 x 10-3
=
=
=
=
=
=
2.41 x 102
6.015 x 103
1.62 x 10-2
5.12 x 10-1
662
.0034
Significant Figures
Significant figures are the
numbers in a measurement that
“matter”.
Rules for determining Significant
Figures
1. All non-zero digits are significant.
1, 2, 3, 4, 5, 6, 7, 8, 9
2. Zeros between non-zero digits
are significant.
(AKA captive or trapped zeros)
102
3 sig figs
7002
4 sig figs
3. Leading zeros (zeros at the beginning
of a measurement) are NEVER
significant.
0.0152
3 sig figs
00542
3 sig figs
4. Trailing zeros (zeros after last
integer) are significant only if the
number contains a decimal point.
210.0 4
0.860 3
524000 3
5240 3
5240. 4
5240.0 5
5. All digits in the coefficient are
significant in scientific notation.
2.1 x 10-5
2
6.02 x 1023
3
6. Exact numbers have unlimited
Significant Figures
Examples:
1 dozen = exactly 12
Examples:
How many significant digits do each of the
following numbers contain:
a) 1.2
b) 2.0
c) 3.002
2
2
4
d) 4600
2
e) 23.450
5
f) 6.02 x 1023
3
Rounding:
 5 round up
< 5 round down (don’t change)
Examples:
Round 42.63 to 1 significant digit = 40
Round 61.57 to 3 sig. digs. =
61.6
Round 0.01621 to 2 = 0.016
Round 65,002 to 2 sig. digs. = 65,000
or 6.5 x104
Addition and Subtraction
– The measurement with the fewest
decimal places to the right of the
decimal point determines the
number of decimal places in the
answer.
Examples:
Solve using correct significant figures
45.756 m + 62.1 m =
75.263 m
+
1123.93 m =
107.9m
1199.19m
Multiplying and Dividing Measurements
- The measurement with the fewest
total significant figures determines
the number of significant figures in
the answer.
Examples:
Solve using correct significant figures:
3.43 m X 6.4253 m =
22.038779 m2
22.0 m2
45.756 m X 1.2 m =
54.9072 m2
55 m2
45.01 m / 2.2 m =
20.45909091 m2
20. m2