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Significant Figures (digits)
How to determine the least significant figure.
How to determine the least significant figure after
mathematical manipulations.
Rules for writing significant figures
All non-zero and digits to the right of any non- zero digit
are significant.
Zeros in a string of zeros to the left of a non-zero digit are
not significant.
0.01120 - has 4 sig figs
320 - has 3 sig figs.
(SIO 1989 convention)
Zeros to the right have meaning (i.e. indicate the precision)
and are obtained during device reading or in mathematical
manipulations
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Rounding Rules
If the digit past the least significant digit
is a:
0 - 4 then “round down” i.e. truncate
5 - 0 then “round up” i.e. add 1 to the
least significant digit and truncate
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Generally there are two types of
devices from which numbers are read
- analogue and digital
Digital devices are simple to determine the least
significant figure. It is the last digit (to the right)
that is read out.
For analogue devices
determine the value that each mark on the device
signifies.
One should be able to estimate one more digit beyond
that designated by the marks.
Rule for writing significant figures
All non-zero and digits to the right of any nonzero digit are significant.
Zeros in a string of zeros to the left of a non-zero
digit are not significant.
<0.01120 - has 4 sig figs
<320 - has 3 sig figs. (SIO 1989 convention)
Zeros to the right have meaning (i.e. indicate the
precision) and are obtained during device reading
or in mathematical manipulations
As an example of an digital device:
a digital balance
125.7283 g
The least significant figure is the "3"
(i.e. read all the digits!)
For an analogue device:
1) Determine what each line value corresponds
to.
2) Estimate one more digit.
0 mL
1 mL
2 mL
2 mL
3 mL
4 mL
5 mL
3 mL
6 mL
7 mL
50 mL
The marks correspond to
0.1 mL
Therefore, one can
estimate to ~0.01 mL
Here read 2.25 mL
If the estimate indicates that the
measurement is on the line, then the
trailing zero must be present
2 mL
3 mL
In this example it appears
that the level in on the
line.
One must indicate the
estimate to ~0.01 mL
Therefore this is 2.50 mL
Rule for multiplication and division
Count the number of significant digits in each
number being multiplied of divided
Example: 524.2
4 significant figures
H 345.725 6 significant figures
181 229.045 Should be to 4 sig figs.
Thus: 1.812 H 105 is the correct answer*.
*note: sometime one must use scientific notation to
express the answer correctly.
Rule for addition and subtraction
1) Determine the uncertainty in each of the numbers.
2) The uncertainty in the answer is the same as the highest
uncertainty determined in step 1)
Example:
34.5
The uncertainty is 0.1 digit
+ 53.25 The uncertainty is 0.01 digit
77.75
But the uncertainty should be with 0.1
digit therefore the answer should be:
77.8
More examples of addition/subtraction
0.1210 The uncertainty is in the 0.0001 digit
-0.01310 The uncertainty is in the 0.00001 digit
0.10790 But the uncertainty should be with the
0.0001 digit, therefore the answer is:
0.1079
1.42 H10-5 The uncertainty is in 0.01H10-5
+ 2 H 10-6 The uncertainty is in 1 H 10-6 digit
1.62H10-5 But the uncertainty should be with the
1H10-6 digit, therefore the answer is:
1.6H10-5