calculations+using+sig+figs

Normal mathematics problems, dealing with exact numbers, usually does not worry about significant figures. Only math dealing with measurements should include significant figures.

There are two rules to remember when using significant figures in calculations involving measurement:
 * 1) When multiplying or dividing, your answer should contain the same significant figures as the problem's least accurate (fewest significant figures) measurement.
 * 2) When adding or subtracting, your answer can only be as accurate as the problem's least accurate number in terms of decimal places.

Example: Density

A person finds the mass of a block of wood to be 39.35 g, and measures its volume to be 37 mL. Density = mass / volume
 * Even though the two measurements are different base units, the answer can still only be reported with two significant figures, because 37 mL only has two significant figures.

D = 39.35 g / 37 mL

Using a calculator will yield an answer of 1.063513514 g/mL, but this must be rounded to two significant figures. Therefore the answer is 1.1 g/mL.

Example: total volume

A graduated cylinder containing 10.0 mL of water is added to a beaker containing 35 mL of water.
 * The volume of water in the beaker is only reliable to the ones place, so the answer will be only reliable to the ones place, and will be 45 mL.

When performing metric to metric unit conversions, the conversion factors are exact, so your answer should contain the same significant figures as provided in the problem.

Example: metric conversions

Convert 100. cm to meters.
 * The conversion factor will be 1 m / 100 cm, which appears to only have one significant figure. But remember that these are exact values, so do not refer to them when working with significant figures.
 * The problem provides the measurement 100. cm, which has three significant figures (thanks to the decimal).
 * The answer will be reported with three significant figures, and is 1.00 m.

When performing English to metric conversions, or vice versa, the conversion factors are not exact and they must be examined for significant figures.

Example: 120 grams = ___ pounds?
 * The conversion factor will look like 1 pound / 453.59 grams. Ignore the 1 pound and use five significant figures from 453.59 grams.
 * The problem provides two significant figures in 120 grams.
 * The answer from a calcualtor will be 0.264556097pound, but we can only use two significant figures; therefore the answer is 0.27 pound.

These significant figure rules will be used in every lab that involves measurement, so be sure to read them over carefully.

Here is a worksheet dealing with significant figures: