Download Notes 2b: Significant Figures

SIGNIFICANT FIGURES IN CALCULATIONS
When you have a floating point number it is usually only good
to a certain number of Significant Figures
35.32956 .125E+13
 Significant Figures are those digits in a number that are
meaningful and correct.
 Digits may not be significant if they are a result of
measurements or calculations involving non significant
digits or because the number has been truncated.
 In a computer all floating point numbers are truncated
because they use a fixed number of bits so they have a
limited number of significant figures.
Some examples:
 12.2537 The last digit that is somewhat meaningful is
sometimes lowered somewhat. This has 5 (6) significant
digits.
 0.00235 3 significant figures because leading zeros are
placeholders to indicate the size of the number . This
could be written as 0.235E-2. So leading zeros are not
significant.
 235000. 6 significant figures. Trailing zeros are
significant (or should be ). You really mean that all the
zeros are meaningful if you write it this way. If not this
should be written .235E+6
Operations with significant digits.
Additions and Subtractions
When adding or subtracting two numbers, the number of
significant figures of the sum or difference depends on the
position of the worst significant digits in the two numbers.
Example 1
128.35
+00.23
=====
128.58
(5 sig. figs.)
(2 sig. figs.)
(5 sig. figs.)
Example 2
128.35
(5 sig. figs.)
+ 1.2x
(2 sig. figs.)
=======
129.5x (4 sig. figs.)
Example 3
128.35
+ 0.000045
==========
129.35
(5 sig. figs.)
(2 sig. figs.)
(5 sig. figs.)
Note in this example the 2nd
number drops out. So you
add two numbers
and get the first
Example 4
Subtraction always dangerous
128.35
- 128.34
==========
000.01
(5 sig. figs.)
(5 sig. figs.)
(1sig. figs.)
So in subtraction can have
real problems
Multiplication and Division
The number of S.F. in the product or quotient is the same as
number of significant figures in the number that has the fewest
significant figures.
Example 1
12.954
x 1.2
======
15.5448
(5 sig. figs.)
(2 sig. figs.)
(2 sig. figs.)
So answers must be meaningful in terms of significant figures.
Real dangers in computing numbers when there is limited
accuracy
1) Adding two numbers of very different size.
2) Subtracting numbers of nearly equal size.