Measurements and Calculations - Chemistry - page 42

Calculating the Volume of a Wood Block

Given
Length = 4.55 cm

shows 3 significant digits

Width = 9.10 cm shows 3 significant digits

Height = 2.54 cm shows 3 significant digits

Volume = L × W × H

Notice that each of our measurements shows 3 significant digits. Because we
are multiplying, we follow the rule for multiplication and division. Therefore,
our answer must show the same number of significant digits as the
measurement with the least number of significant digits.

Volume = 4.55 cm × 9.10 cm × 2.54 cm = 105.1687 cm 3

We must round to the ones place. We look to the right of the ones place and
we see a “1,” which tells us to round down. Our final answer becomes:

Volume = 105 cm 3

Figure 2-4b

Now, our answer no longer claims to be more accurate than the mea-
surements that it was based on. Figure 2-4b illustrates the rule for round-
ing after multiplication. Each of the measurements showed only three
significant digits, so the calculated volume could only show three signifi-
cant digits.
Before we move on to the next lesson, let's go over an example of the use
of the rule for addition and subtraction. Imagine that you wanted to find the
mass of a sample of water in your chemistry laboratory. You can't just pour
the water onto the balance, so how would you do it? First, you would find
the mass of an empty vessel, perhaps a graduated cylinder. Then, you would
add the water to the graduate, and mass it again. Finally, you would sub-
tract the mass of the empty graduate from the mass of the full graduate,
and the difference would represent the mass of just the water. When you
got your final answer, you would round according to the number of deci-
mal places in your measurements, as demonstrated in Figure 2-4c.