Making the number of significant figures apparent reporting a large number.
Tailing zeros that appear to the
RIGHT of the decimal point in reported numbers
are significant (0.0120 has three significant figures).
Tailing zeros that appear to the
LEFT of the decimal point
are not necessarily significant.
Example: A reported measurement of 350 g may have either two or three signficant figures.
Example: A reported measurement of 57 400 kg may have 3, 4 or 5 significant figures
The potential ambiguity may be avoided by using scientific notation.
Example: A measurement reported as 3.5 × 102 g clearly has two significant figures.
Example: A measurement reported as 3.50 × 102 g clearly has three significant figures.
Significant figures to be reported for numbers calculated by multiplying or dividing measurements
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.
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.
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.
Significant figures to be reported when the numbers are added or subtracted
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.
Significant figures to be reported when an average is calculated
It is common practice to repeat measurements and then to report an average of these results. This involves both addition and division by a pure number.
Because division by a pure number does not change the number of significant figures,
the average is reported to the
number of significant figures in each measurement.
Example: The titres for four different titrations were 25.68
, 25.75
, 25.59
.
The calculated average of these titres is 25.673333333
This should be reported as 25.67