http://www.ck12.org Chapter 1. Introduction to Physical Science
and which are estimated? How can you tell how many significant figures there are in the measurement? There are
several rules for counting significant figures:
- Leading zeros are never significant. For example, in the number 006.1, only the 6 and 1 are significant.
- Zeros within a number between nonzero digits are always significant. For example, in the number 106.1, the
zero is significant, so this number has four significant figures. - Zeros that show only where the decimal point falls are not significant. For example, the number 470,000 has
just two significant figures (4 and 7). The zeros just show that the 4 represents hundreds of thousands and the
7 represents tens of thousands. Therefore, these zeros are not significant. - Trailing zeros that aren’t needed to show where the decimal point falls are significant. For example, 4.00 has
three significant figures.
Q:How many significant figures are there in each of these numbers: 20,080, 2.080, and 2000?
A:Both 20,080 and 2.080 contain four significant figures, but 2000 has just one significant figure.
Determining Significant Figures in Calculations
When measurements are used in a calculation, the answer cannot have more significant figures than the measurement
with the fewest significant figures. This explains why the homework answer above is wrong. It has more significant
figures than the measurement with the fewest significant figures. As another example, assume that you want to
calculate the volume of the block of wood shown below.
The volume of the block is represented by the formula:
Volume = length×width×heightTherefore, you would do the following calculation:
Volume = 1.2 cm×1.0 cm×1 cm = 1.2 cm^3Q:Does this answer have the correct number of significant figures?
A:No, it has too many significant figures. The correct answer is 1 cm^3. That’s because the height of the block has
just one significant figure. Therefore, the answer can have only one significant figure.