What is the use of learning significant figures?

Answer 1

Significant figures are used often in science. The number of numbers in the answer informs us succinctly how well or how precisely we know an answer. Typically, a number with few significant figures reflects measurements made with cheap or imprecise equipment, while a larger number of significant figures indicates a more careful measurement using fancier (more precise) equipment.

Measurement is always a compromise. You want the "best" numbers you can get, but you do not have infinite time nor infinite money to get that information. (An additional significant figure can cost ten times more than the previous one, and can take twice or more time to do the measurement.)

The scientist's art lies in using instruments that are good enough to yield an answer that is accurate enough to decide the question (the hypothesis). You actually make decisions like this one every day. Say, for instance, you want to decide whether you can move your table from your kitchen to your bedroom. Question: is there enough space in your bedroom? First, you "eyeball" the table and the space. If there obviously is enough room, you move the table. But what if you don't know? Well, then you probably use your arms to guess the sizes. If you still can't decide, then you would go get the ruler or tape measure to decide once and for all. As you went through this process, you went from an imprecise measurement to ever more precise measurements, until you were able to decide. You did the easy measurement (eyeball) first because it takes the least time and it could have answered the question easily.

The same concept applies to science. We do not automatically use the fanciest equipment we have - that would be a waste of time and money. Instead, we try to use the equipment that will give us a "good enough" answer quickly.

The result of these measurements is summarized in the significant figures in our answer. For example, a beaker might be able to tell us that we have 25 mL. If that is as precise as we have to get then the beaker is OK. If, however, we need a more precise answer, we might use a graduated cylinder, which might give us 25.2 mL, or a buret, which might give us 25.18 mL, if we need to know the volume that precisely. Note the approximate volume (25 mL) is the same - the difference is that we know that volume more or less accurately, depending on our need. The beaker gave us 2 significant figures (because it is not very precise). The graduated cylinder gave us 3 significant figures, and the buret gave us 4 significant figures. (The graduated cylinder usually costs more and takes longer to read, and the buret costs still more and takes an even longer time to read.)

So the answer is that we use significant figures as a shorthand way of telling each other how carefully we made the measurement. Generally 3 significant figures is a typical laboratory measurement, and 6 significant figures often reflects a research university measurement.