Alex, Alexis, Jordan and Whitney were in attendance. We started out by reviewing the precision reporting rule for adding and subtracting:

add/subtract rules

The people who were there wanted an example right away, so I used 12.5 + 3.26, which adds to 15.76. Since 12.5 is only known to the precision of the nearest 0.01, we have to round our answer to the nearest 0.01, as well. This means we should actually report an answer of 15.8.

adding examples

Next, I gave examples of adding and subtracting:

subtracting examples

In the first adding example, we round to the nearest 0.01, because that is the precision of both the measurements being added. In the second example, we round to the nearest 10, because that is the precision of the least precise of the two measurements, 30, which is written without a decimal point. The only adequate way to report this precision is with scientific notation, so it is written as 3.0 x 10².

In the first subtraction example, the answer is rounded to the nearest 0.1, because the least precise measurement, 1.2, is only known to the nearest 0.1. In the second subtraction example, the answer is rounded to the nearest 1, because that is the precision of 2, which is the least precise of the measurements.

Next, we reviewed the precision reporting rule for multiplication and division:

multiply/divide rules

Right after that, I showed examples for multiplication and division:

multiplication examples

In the first multiplication example, the answer is rounded to 2 sig. figs. because the least precise measurement, 3.0, shows only 2 sig. figs. In the second multiplication example, the answer is rounded to 1 sig. fig. because the least precise measurement, 4, shows only 1 sig. fig.

division examples

In the first division example, the answer is rounded to 2 sig. figs. because the least precise of the two measurements, 4.0, is shown to only 2 sig. figs. In the second division example, the answer is rounded to 3 sig. figs. because both measurements have 3 sig. figs.

Practice Problems

Last, I posted 4 practice problems:

Try them yourself. See if you get the right answer by checking here.