SIGNIFICANT FIGURES AND FACTOR-UNIT CALCULATIONS

Almost all scientific study involves some type of measurement. Every measurement has some degree of uncertainty. This degree of uncertainty is dependant upon the device or technique that is used to make the measurement. The uncertainty in measurements is indicated in the numbers used to report the scientific measurement.

Equipment used in the general chemistry laboratory can be read to within the smallest indicated subdivision (mark) on the equipment with ease. With most equipment, a final digit between scale marks may be estimated. The numbers used to represent the certain numbers plus the one estimated number are called significant figures or digits. When you record a measured value, it is important that the measurement is stated to the proper number of significant figures. Numbers obtained by counting or those that are part of a definition (e.g., 1 kg = 2.2 lb.) are called exact numbers and have an unlimited number of significant figures.


Use the following rules for deciding the number of significant figures in a measured quantity:

(1) All nonzero digits are significant.

(2) Zeroes between nonzero digits are significant.


(3) Zeroes to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point.

(4) Zeroes to the right of a decimal point in a number are significant.

0.20 has 2 significant figures

0.02 has one 1 significant figures

(5) When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant:

2020 inches may have 3 or 4 significant figures

10,250,000 miles may have 4, 5, 6, 7, or 8 significant figures


Confusion about rather significant figures in rule (5)  can be avoided by the use of scientific notation. For example, depending on how many significant figures we wish to express we may write the number 10,250,000 miles as:

1.0250000 x 107 (8 significant figures)

1.025000 x 107 (7 significant figures)

1.02500 x 107 (6 significant figures)

1.0250 x 107 (5 significant figures)

1.025 x 107 (4 significant figures)

Calculations involving significant figures: It is important to be able to express answers from calculations to the correct numbers of significant figures in order for the result to be meaningful. If calculations are done using a calculator, the answer frequently has more significant figures than are justified. Therefore, it is important for you to be able to determine how many significant figures are allowable and how to round the answer to give you the proper number of significant figures.

Additionally, it may be necessary at time to convert a quantity from one unit to another. The simplest way to perform these calculations is to use the "unit-factor", "factor-unit", or "factor-label" method. In the unit-factor method a quantity in one unit is multiplied by a conversion factor. It is important when using the factor-label method that the equation is set up to that the unwanted unit(s) cancel. For example:

When converting lbs. to grams you would use the conversion factor 454 g / 1 lb rather than 1 lb / 454 g

Use the following steps to solve problems using the factor-unit method:

1. Identify the given quantity and its unit.

2. Determine (by thinking) about how you can change units from the given units to the units required by the answer. Determine the conversion factor for each change.

3. Set up the problem. Arrange conversion factors to cancel units. Make sure all units cancel.

4. Carry out calculations to appropriate number of significant figures.