#### Significant Figures

Lovingly dubbed "sig figs" by many chemists, significant figures are a way to round long numbers. There are two rules to remember when counting how many significant figures appear in a number. If there is a decimal point present, start counting sig figs from the first non-zero number on the left. For example, 56.90 has four sig figs, while 59.0 has three. If there is no decimal point present, start counting sig figs from the right-most non-zero number. For example, 3200 has 2 sig figs, while 1643 has four. To add and subtract, the final answer should have the same number of decimal points as the number with the fewest decimal points in the problem. For example, 42.3-10.00=32.3 (since 42.3 has one number after the decimal, the final answer also only has one). To multiply and divide, the final answer should have the same number of total significant figures as the number with the fewest sig figs. For example, 4x12.0=50 (since 4 only has one sig fig, the answer should only have one as well).

#### Density

Density is a  way to measure how compact a substance is, or how much matter is present within a given space. To solve for the density of an object use the equation: Density=mass/volume. The equation can be rearranged to solve for mass or volume if density is known.

#### Scientific Notation

Scientific notation is a way to make extremely large or extremely small numbers more manageable. To write a number in scientific notation, first move the decimal point in the number to a value between 1 and 10, such as 1.4 or 8.5. Then count the number of spaces that you moved the decimal point and multiply the number between 1 and 10 by 10 raised to the power of the number of decimal points counted. If the decimal was moved to the left, the exponent should be positive; if the decimal was moved to the right, the exponent should be negative. For example, 45,000 becomes 4.5 x 10^4. Or, 0.0076 becomes 7.6 x 10^-3

#### States of Matter

Matter can be classified into solid, liquid, and gas states. In a solid, molecules are very compact and are unable to move very much, causing the solid to maintain its shape. In a liquid, the molecules are more free to move around and can conform to the shape of a vessel. In a gas, molecules are completely free to move and thus spread out in all directions, diffusing to fill any space.

#### Separation of Mixtures

Separation of mixtures is an extremely important process in chemistry. Outlined below are certain common ways of separating mixtures:

1. Separation by hand - large, solid pieces of a certain substance present
2. Magnetism - iron or other magnetic compound present
3. Filtration using filter paper, funnel, and distilled water - water soluble compounds can flow through the filter paper while water insoluble compounds will remain trapped in the filter paper.
4. Evaporation/simple distillation - Drying the filter paper from the previous method will leave just the water-insoluble compounds in the mixture. Additionally, leaving a solution in which a solid has dissolved in liquid to evaporate will yield just the dissolved solid.
5. Boiling point/fractional distillation - in a mixture of liquids, an apparatus of a hot plate, vertical tube, and condenser can be used to separate liquids that turn from liquid to gas at different temperatures
6. Crystallization - heating a solution in which a solid is dissolved then cooling it while reducing solubility will yield a pure solid crystal

#### Chemical and Physical Changes

Chemical and physical changes constantly occur in the world around us. Chemical changes occur when there is a change at the atomic level as the result of a chemical reaction. For example, a reaction between baking soda (sodium bicarbonate) and vinegar (acetic acid) produces bubbles (a release of carbon dioxide gas). This reaction takes place at the atomic level, thus making it a chemical change. Other common examples of chemical changes include a nail rusting or baking a cake. Contrastingly, physical changes occur when state of matter changes or when shape or size change. For example, crushing a can is a physical change because only the size/shape have changed and the molecular composition remains the same. Other common examples of physical changes are boiling water, breaking glass, or dissolving sugar in water. Most of the time, chemical changes are hard to reverse while physical changes are easier to reverse, but this is not a perfect rule to tell the difference. Rather, consider whether you could write a chemical equation for the process that takes place

#### SI Units of Measurement

Both precision and accuracy are important in the study of chemistry, but each word has a slightly different meaning. As shown in the image, precision means obtaining repetitive and consistent results, even if they are not necessarily correct. Contrastingly, accuracy denotes a more "correct" set of data, even if the points are more spread out.

(Image Courtesy of: https://wp.stolaf.edu/it/gis-precision-accuracy/)

#### SI Units of Measurement

The basic units of SI (Système Internationale/International System) are the meter, gram, and second. The beauty of SI measurement lies in the ease of transfer between orders of magnitude of measurements. Each prefix in the SI system represents a multiple of 10 from the basic meter/gram.

(Image Courtesy of: https://www.craftsmanspace.com/knowledge/international-system-of-units.html)