# Numbers in Chemistry

## Metric System, Scientific Notation, Dimensional Analysis, Density

We are going to focus on using your calculator when working with scientific notation. The first few practice problems we will do will "move the decimal" going back and forth from regular notation to scientific notation. However, as the picture represents, we will learn that scientific notation numbers are just like any other number and using your calculator correctly will insure success.
1.8 Scientific Notation on the calculator

## Significant Figures

You may have caught on through the lab that the equipment you use limits the accuracy of a calculation. For example, a metric ruler typically measures to 1 mm or 0.001 m (0.1cm). If you use a balance to measure the mass of a cube and the balance measures to 3 decimal places but the ruler you used to measure the length of the cube measures to 0.1 cm, then the density calculation can only be reported to one decimal place, not the 6 or 7 decimal places your calculator shows. The rules in the figure below point out some pretty picky "zero rules" but they can be summed it: If the number is greater than one and there is a DECIMAL, everything is significant. If the number is less than one, do not count the "placeholder" zeros after the decimal but count all digits after the zeros. If the number has no decimal and ends in zero(s), do not count the zero(s) at the end of the number.

## Metric system

The metric system is the only system used in scientific fields. The figure below shows the "prefixes" for the powers of ten that each represents. The figure on the right shows the most important examples of metric prefixes. Memorize these prefixes because you need to be completely comfortable with this system. We will work numerous problems to help you along.

## Dimensional Analysis

You may have seen this method for solving problems before (picket fence, etc) but STOP RESISTING using this method because it makes everything so much easier! You can solve many problems in chemistry and physics by focusing on the UNITS instead of randomly punching numbers into your calculator until you get one of the multiple choice answers. By the way, mean instructors such as myself are on to this student method and incomplete answers (answers to part of the problem) are there to distract you on a test. So climb on the unit bandwagon and be more confident in your problem solving!
Dimensional Analysis

## Density

You have probably used the density formula several times over the years you have been in school. It is not uncommon, however, for students to be in college and still not have a firm grasp of this concept. The picture above shows the particle view of density. Once students understand this concept AND then master the units for density, they do, then, understand density. Density is a ratio of mass and volume and as you may have found in the lab, the size of the sample for a particular material does not change the density because it is how those particles are arranged and the ratio, therefore, does not change. The units are g/mL if working with liquids; g/cubic centimeter if working with solids (mL = cubic centimeter).