When measurements are multiplied or divided, the number of
significant figures in the
overall answer should be no greater than the smallest number in the given data.
Example: 25.00
of 0.105
is titrated exactly with 27.52
aqueous NaOH.
The calculated concentration including all digits from the calculator is 0.09538517442
.
This concentration should be reported as 0.0954
because one of the values used in its calculation is only known to three significant figures.
When measurements are added or subtracted,
the number of
significant figures in the
answer is limited by the number with the fewest decimal places.
Example: The length measurements 1.0 m, 0.025 m and 2.10 m add to give 3.125 m.
This should be reported as 3.1 m because one of the measurements has a single digit to the right of the decimal point.
When an average is calculated This involves summing the values and dividing by a pure number. Division by a pure number does not change the number of significant figures.
Therefore the rule for addition applies to this case
Example: The titres for three different titrations were 25.68
, 25.75
, 25.59 mL.
The average is calculated by adding the three titres and dividing the sum by the number of titres (3).
The calculated average of these titres is 25.673333333
. This should be reported as 25.67
VERY IMPORTANT!! For multistep calculations, carry through all digits (significant or not!!) in intermediate values and round ONLY at the end to the number of significant figures consistent with the given data.