Calculations
Uncertainty
In Calculations
Measured
quantities are often used in calculations. The precision of the calculation is
limited by the precision of the measurements on which it is based.
Addition
and Subtraction|
When measured quantities are used in addition or
subtraction, the uncertainty is determined by the absolute uncertainty in the
least precise measurement (not by the number of significant figures). Sometimes
this is considered to be the number of digits after the decimal point.
Example
32.01 m
5.325 m
12 m
Added together, you will get 49.335 m, but the sum should be reported as '49'
meters.
Multiplication
and Division
When
experimental quantities are mutiplied or divided, the number of significant
figures in the result is the same as that in the quantity with the smallest
number of significant figures. If, for example, a density calculation is made in
which 25.624 grams is divided by 25 mL, the density should be reported as 1.0 g/mL,
not as 1.0000 g/mL or 1.000 g/mL.
Significant
Figure Rules
- Non-zero
digits are always significant.
- All
zeros between other significant digits are significant.
- The
number of significant figures is determined starting with the leftmost
non-zero digit. The leftmost non-zero digit is sometimes called the most
significant digit or the most significant figure. For example, in the number
0.004205 the '4' is the most significant figure. The lefthand '0's are not
significant. The zero between the '2' and the '5' is significant.
- The
rightmost digit of a decimal number is the least significant digit or least
significant figure. Another way to look at the least significant figure is
to consider it to be the rightmost digit when the number is written in
scientific notation. Least significant figures are still significant! In the
number 0.004205 (which may be written as 4.205 x 10-3), the '5'
is the least significant figure. In the number 43.120 (which may be written
as 4.3210 x 101), the '0' is the least significant figure.
- If
no decimal point is present, the rightmost non-zero digit is the least
significant figure. In the number 5800, the least significant figure is '8'.
Significant
Figures and Calculations
Classification
of Matter
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