significant+figures

A //significant figure// is a number in a reported measurement that has credibility - it is there for a reason.

The more significant figures there are in a measurement, the more accurate that measurement is. However, the number of significant figures a measurement has is limited to the accuracy of the device.



For example, suppose a volume of water is collected using a 100 mL beaker, and its volume is reported as 35 mL.
 * This measurement - 35 mL - has two significant figures.

Suppose the 35 mL of water is transferred into a 100.0 mL graduated cylinder, and now the volume of water is reported as 38.3 mL.
 * Now the accuracy of the measurement has increased, and the measurement has three significant figures.

Finally, the water is poured into a buret, and the volume of the water is recorded as 38.27 mL.
 * This measurement is the most accurate of the three, having four significant figures.

As you can see, the more certain numbers a measurement has, the more accurate that measurement is. But what about zeros?

Here are **four rules to follow** when it comes to determining how many significant figures a measurement has: Here are some examples on how to use these rules.
 * 1) All non-zero numbers are considered significant;
 * 2) All zeros between significant figures are significant;
 * 3) Any zeros to the right of a decimal AND a significant figure are significant;
 * 4) A zero may be shown to have significance using a decimal, a bar over it, or by converting to scientific notation.

Example 1: a building is 440 meters tall.
 * There are two non-zeros - the fours - therefore they are significant.
 * The last zero is not marked with a decimal or a bar, and is therefore not significant.
 * There are two significant figures in the measurement 440 m.

Example 2: a bottle holds 505 mL of water.
 * The two fives are significant.
 * The zero between them is therefore significant.
 * There are three significant figures in the measurement 505 mL.

Example 3: a brass weight has a mass of 50.00 g.
 * The five is significant.
 * There is a decimal, and a non-zero (the five), with zeros to the right of both. Therefore both the end zeros are significant.
 * The zero at the ones place is now between significant figures and is also significant.
 * There are four significant figures in the measurement 50.00 g.

Example 4: The volume of a lake is 2,000,000. liters.
 * The two is significnant.
 * There is a decimal at the end of the number, making that zero at the ones place significant.
 * All the remaining zeros are betweeen significant figures, and are all significant.
 * There are seven significant figures in the measurement 2,000,000. L.

If the volume of the lake was reported as 2,000,000 L (without the decimal) then there would only be one significant figure (the two), so that would be a much less accurate measurement.



To put significant figures in perspective, consider the term "uncertainty". Every measuring device has an uncertainty, which is just a way of describing its accuracy. Usually the last acceptable or certain number in a measurement is its "uncertain" value, but is considered an educated guess.

A large beaker has an uncertainty of plus or minus 5 percent, so if you measure 50 mL, you may actually only get 47 mL, or you might get 53 mL. So to properly (accurately) report the measurement, you can only be certain of the tens place (and the zero in the ones place is not certain - not significant).

With a graduated cylinder, there are individual milliliter markings. This means you can estimate inbetween these markings, which would be to the tenth of a milliliter. So a measurement of 50 mL should be reported as 50.0 mL, and may actually only vary by 0.1 mL. So you could actually have 49.9 mL or 50.1 mL, which is quite a bit more accurate than the beaker.

To sum it all up, we keep track of significant figures so that we are reporting our measurements with the proper accuracy, within the acceptable limits of the device's uncertainty.

Here's some practice: