Significant Figures Example Problem

Here are three examples determining significant figures. When asked to find significant figures, remember and follow these simple rules:

• Any nonzero digit is significant.
• A zero between two nonzero digits is always significant.
• Trailing zeros are significant if they are at the end of a number and to the right of the decimal point.
• Leading zeros to the left of the first nonzero digit are not significant. For example, "placeholder" zeros in the number 0.005 are not significant (only the 5 is significant).
• If a number ends with a zero, but it is not to the right of a decimal point, it may or may not be significant. Generally, it's safest to assume it is not significant. If you take a measurement where the final zero is significant, be sure to include the decimal point to make yourself clear.

Three students weigh an item using different scales. These are the values they report:

a. 20.03 g
b. 20.0 g
c. 0.2003 kg

How many significant figures should be assumed in each measurement?

Solution

a. 4.
b. 3. The zero after the decimal point is significant because it indicates that the item was weighed to the nearest 0.1 g.
c. 4. The zeros at the left are not significant. They are only present because the mass was written in kilograms rather than in grams. The values "20.03 g" and "0.02003 kg" represent the same quantities.

Answer

In addition to the solution presented above, be advised you can get the correct answers very quickly by expressing the masses in scientific (exponential) notation:

20.03 g = 2.003 x 10¹ g (4 significant figures)
20.0 g = 2.00 x 10¹ g (3 significant figures)
0.2003 kg = 2.003 x 10^-1 kg (4 significant figures)