Significant Figures
It is important to determine the number of significant figures properly because in science, numbers that have importance must be considered, while meaningless numbers are best left ommited. Scientific values should be expressed in reasonable ways.
In the first sample number, 0.0034g, there are only 2 significant figures. Since one of the rules of determining significant figures states that all non-zero numbers are significant, we can safely state that the numbers 3 and 4 (0.0034)are indeed significant. Place-holding zeros are not considered to be significant, and in this case all the zeros to the left of the 3 and the 4 (0.0034) are place-holding, and therefore not significant.
The second sample number 150.0 has 4 significant figures. As stated above, all non-zero numbers are significant, so we know that the 1and the 5 are significant. Now we must consider the zeros, which are not place-holding zeros. There is another rule when dealing with significant figures that states that zeros that fall to the right of a decimal point are significant, so that means that the final zero in the sample number (150.0) is also significant. Finally, zeros between significant digits are significant too, so the first zero (150.0) is also considered significant. That totals up to 4 significant figures.
In the final sample number, 120 yd, it is not clear how many significant figures there are. Usually we say there are only two, because all trailing zeros in a whole number are not considered significant. However, they could still be significant. When numbers like these occur they are commonly expresed in scientific notation to prevent any confusion. For example, the number 120 can be written in the form 1.2x102 to specify that it has only 2 significant figures. It can be written as 1.20x101 if it needs to be expressed in 3 significant figures.
Scientific notation is important to help determine the number of significant figures and also to maximize precision. It also simplifies the way we deal with extravagant numbers.
