Your calculated value cannot be more precise than the least precise quantity
used in the calculation. The least precise quantity has the fewest digits to the
right of the decimal point. Your calculated value will have the same number of
digits to the right of the decimal point as that of the least precise quantity.
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.
Answer not rounded-->
Answer not rounded-->
Rounded to least number
of decimal places-->
Rounded to least number of decimal
Multiplication and Division
of significant figures in the final calculated value will be the same as that of
the quantity with the fewest number of sig figs used in the calculation.
Remember to follow the order of operations. Be sure to
remember to include only the sig. figs. before going on to the next operation.
Losing Significant Figures
Sometimes significant figures are 'lost' while
performing calculations. For example, if you find the mass of a beaker to be
53.110 g, add water to the beaker and find the mass of the beaker plus water to
be 53.987 g, the mass of the water is
53.987-53.110 g =
The final value only has three significant figures, even though each mass
measurement contained 5 significant figures.
Rounding and Truncating Numbers
There are different methods which may be used to round numbers.
The usual method is to round numbers with digits less than '5' down and numbers
with digits greater than '5' up (some people round exactly '5' up and some round
If you are subtracting 7.799 g - 6.25 g your calculation would yield 1.549 g.
This number would be rounded to 1.55 g, because the digit '9' is greater than
In some instances numbers are truncated, or cut short, rather
than rounded to obtain appropriate significant figures. In the example above,
1.549 g could have been truncated to 1.54 g.
Sometimes numbers used in a calculation are exact rather than
approximate. This is true when using defined quantities, including many
conversion factors, and when using pure numbers. Pure or defined numbers do not
affect the accuracy of a calculation. You may think of them as having an
infinite number of significant figures. Pure numbers are easy to spot, because
they have no units. Defined values or conversion factors, like measured values,
may have units. Practice identifying them!
You want to calculate the average height of three plants and measure the
following heights: 30.1 cm, 25.2 cm, 31.3 cm; with an average height of (30.1 +
25.2 + 31.3)/3 = 86.6/3 = 28.87 = 28.9 cm. There are three significant figures
in the heights; even though you are dividing the sum by a single digit, the
three significant figures should be retained in the calculation.