Non-Measured Quantities

Reference > Science > Significant Figures

In the next section, we're going to deal with multiplying and dividing numbers, and determining the significant figures of the result. Before we do that, however, we need to establish that there is a difference between a measured quantity and a non-measured quantity.

The number pi, for example, is a mathematical constant. It's not a measured quantity. How many significant digits does it have? It has an infinite number of significant digits!

However, if your calculator only handles 8 digits, then you're using an approximation of pi, which has 8 significant digits.

And, if you decide to approximate pi as 3.14, then you've limited the number of significant digits to 3. And if you've limited the number of sig figs in the number pi, then you've also limited the number of sig figs in any calculations that use that approximation.

For this reason, it's a good idea, whenever possible, to use your calculator's value of pi, rather than an approximation, so there is no loss of precision.

Aside from pi, there are other non-measured quantities we may use in doing sig fig calculations. Consider the following formula, which is the formula for the perimeter of a rectangle: P = 2L + 2W.

In this formula, the number 2 is a non-measured constant. If it was a measured value, we would say it has one significant digit. But since it's not measured, we say that it also, like pi, has an infinite number of significant digits. It might help you to think of it as 2.00000....

Other formulas have non-measured quantities as well. Here's the volume of a sphere: V =

πr³. The constant pi, and the value

are not a measured quantities. The value of

is 1.333..., and it has infinitely many significant digits. However, if you round it to 1.33, you've limited your precision to three significant digits. Again, as with pi, it's a very good idea to use your calculator's value for

, rather than a rounded value.

In addition to mathematical constants and formula coefficients, there are other quantities that are considered to be non-measured. These are values that we obtain by counting. If I count the number of blocks in a tower, and I find that there are 25 blocks, that is not a measured quantity; it is a counted quantity. Like all the other non-measured values we've discussed here, it has infinitely many significant figures. It is 25.000.... Because we counted, we know that the result is exactly one of the counting numbers, without any estimating. There isn't 25.1 blocks, or 25.000003 blocks. It is exact. Thus, we consider it to be as precise as we need it to be for our calculations.