Download Significant Figures

CH6A
SIGNIFICANT FIGURES
INSTRUCTOR: J.T.,
P: 1
Numbers:
I. Exact numbers (have an infinite number of significant figures.)
a) Counted Numbers (Example: 10 atoms, 9 planets)
b) Defined Numbers, come from definitions within a system of units.
(Example: 100 cm = 1 meter; 1 gallon = 4 quarts)
II. Inexact numbers:
They come from measurements. (The exactness of any measured numbers is
expressed by the number of significant figures (digits)
Measured numbers are usually reported in such a way that only the last digit is uncertain.
4.123
6 g
7
When you use an analytical balance you will see:
(Example: 4.1236 g has 5 s.f., the last digit is uncertain!)
III. The significant figures of Numbers: Identifying S. f.:
1) All non-zero digits, count as S.f. count as S.f. (Example: 128736, has 6 s.f.)
2) Captive Zeros (zeros between two non-zero digits), count as S.f. count as S.f. (Example:
23.450083, has 8 s.f., )
3) Leading zeros (Example: 0.0004568, has 4 s.f.,), never count as S.f.
4) Trailing zeros in a number containing a decimal point., count as S.f. (Example:
456.5600, has 7 s.f., )
5) Trailing zeros in a number NOT containing a decimal point can be ambiguous! (Example
328000). The zeros may or may not be significant.
IV. Rounding:
If you are rounding a number to a certain degree of significant digits, and if the number
following that degree is less than 5 the last significant figure is not rounded up, if it is greater
than
5 it is rounded up.
Examples:
A) 24.4760 rounded to four significant figures is 24.48
B) 24.4740 rounded to four significant figures is 24.47
CH6A
SIGNIFICANT FIGURES
INSTRUCTOR: J.T.,
P: 2
V. Arithmetic:
1) Multiplication and division: the result should have as many significant digits as the
measured number with the smallest number of significant digits.
Example 1:
34.5282
×
(6 s.f.)
21.32 = 736.14122 → 736.1
(4 s.f.)
(4 s.f.)
Smallest
Example 2:
37.425
(5 s.f.)
÷
2.45 =
15.27551 → 15.3
(3 s.f.)
(3 s.f.)
Smallest
2) Addition and subtraction: the result should have as many decimal places as the measured
number with the smallest number of decimal places (d.p.).
Example 1:
23.6318 + 26.56 + 9.87924 = 60.07104 → 60.07
(4 d.p.)
(2 d.p.)
(5 d.p.)
(2. d.p.)
Smallest
3) Significant figure rules for logarithms:
Log A = B
The total number of s.f. given in B after decimal point must be equal to the total number
of s.f. in the A.
Example: - log (0.000016) = 4.07
In exponential form:
10B =A
(the total number of s.f. in A must be equal to the total number of s.f. in
B after decimal point.)
CH6A
SIGNIFICANT FIGURES
INSTRUCTOR: J.T.,
P: 3
Examples I:
NUMBER
NOTE
# SIGNIFICANT FIGURES
48,923
5
3.967
4
900.06
5
0.0004 (= 4 E-4)
*
1
8.1000
5
501.040
6
3,000,000 (= 3 E+6)
**
1
10.0 (= 1.00 E+1)
***
3
(*)
(**)
(***)
0.0004 = 4 × 10 −4
3,000,000 = 3 × 10 +6
10.0 = 1.00 × 10 +1
Example II:
14
The Bottom of
the Concave
Meniscus
15
•
•
•
•
•
The smallest division in this buret is 0.1 mL.
The reading error is 0.01 mL.
An appropriate reading is 14.26 mL
The number of significant figures is 4, (3 digits with certainty and the last digit with uncertainty.)
The correct final record: 14.26 ± 0.01