|
The basic rule for deciding how many significant digits there are in a
number that you are reading is the same. Count every digit that
was actually measured. The only digits not counted are zeros whose sole function is
holding the decimal place. There are some examples of finding how many significant
digits in various numbers shown in Example 3 in your workbook. Let's look them over. |
418 g
3.82 mL
|
The first two are pretty straight forward: 418 grams contains 3
significant digits; 3.82 milliliters contains 3 significant digits also. Notice that the
position of the decimal point is not a factor in determining how many significant digits
there are in a number. |
4.002 kg
|
In the next one, 4.002, the zeros are significant digits. They're not
there to hold the decimal point; they are there to show that zeros were measured. The 4
was measured; the zeros were measured; then a 2 was measured in the last place. All of
those digits were measured. |
| 741.80 g |
The next one, 741.80 grams, contains 5 significant digits. The zero is a
significant digit. It is not there to hold a decimal point. The zero is there to show
precision. The only reason for writing down that zero is to show that it was measured. |
| 0.003 m
(= 3 mm) |
The leading zeros in the next measurement (0.003 m) are holding the
decimal point to show size. They are not significant digits. Nothing was actually measured
until the 3 showed up. If this value were measured in millimeters, the value would be 3
mm. Notice how the zeros disappear? They are no longer needed, they were for size rather
than for precision. |
| 74000 g
74000 g
(= 74.0 kg)
|
The next value (74000 g) returns us to the dilemma of the zeros. Certainly
the 7 and the 4 are significant digits. Some or all of the zeros might be,
depending on how precisely the measurement was made. There are at least two and perhaps as
many as five significant digits. Since there is doubt, just say there are two. This
dilemma could have been avoided in several ways by the person who recorded this
measurement. I could have said it was measured to the nearest 100 g. I could have said
it was measured with three significant digits. I could have used kilograms instead of
grams, then the place-holding zeros would not have been needed. Or I could have used
scientific notation, which I will tell you about later in this lesson. |
