Numbers    

    To be able to use quantitative physical properties, it is important to be fluent with the metric system. The following is a table of the most common prefixes:

    The following figure is useful for metric conversions:

    Typicall scientific numbers are so large and require high levels of precision. As a result, scientific notation is often used. The rules are

Rules for Scientific Notation

1. non-zero digit is placed before the decimal
2. about 2-5 digits are placed after the decimal
3. "X 10" to the appropriate exponent is placed after the number--if you have to move the decimal to left, exponent is more
   positive and if you move decimal to right, exponent is more negative

e.g. express the following numbers in scientific notation:

• 1994 = 1.994 X 10³
• 0.051 = 5.1 X 10^-2
• 6.75 = 6.75 not 6.75 X 10⁰as 10⁰ is always omitted

    Note that the EXP button on calculator = "X 10" thus hit EXP before typing the exponent (if you don't have a calculator, convert all numbers to same exponent and subtract exponents if dividing, add exponents if multiplying or keep same exponent if adding/subtracting).

Classification

    The need to classify is inherent in humans.  It makes our lives easier by allowing us to know something about a wide variety of things and allows us to make predictions about things we do not know much about.  Classification is usually part of the early stages of understanding science.  It allows us to sort our data into unifying categories so that we can wrestle with "what it means" in a more efficient manner.  A chemist will usually classify all "stuff" that has "substance", i.e. matter.  The classification scheme currently used, although seemingly straightforward, is the result of centuries of investigation and thought!  Matter can be described empirically (directly observed) or inferentially (implied based on properties). Empirical is typically where we start since these descriptions or definitions only rely on our senses to understand the world.

    One way to describe matter empirically is by using a structural definition in that the matter is observed in an unchanging condition and described. Consider the states of matter.

    All substances have properties that we can use to identify them.  For example we can identify a person by their face, their voice, height, finger prints, DNA etc..  The more of these properties that we can identify, the better we know the person. I n a similar way matter has properties - and there are many of them.  There are two basic types of properties that we can associate with matter. These properties are called physical properties (do not change the chemical nature of matter) and chemical properties (do change the chemical nature of matter).  Physical properties can be classified as quantitative (measurable) or qualitative (not measurable), but more importantly they can be identified as either intensive (do not depend on the amount of the matter present) or extensive (change with the amount of matter present). Examples of intensive properties include color, odour, luster, malleability, ductility, conductivity, hardness, melting/freezing point, boiling point and density.  Examples of extensive properties include mass, weight, volume or length.  Examples of chemical properties are: heat of combustion, reactivity with water, pH, and electromotive force.

    Chemical properties tend to also be operational properties in that they can only be observed as a result of change. For example, you cannot tell just by looking at iron or aluminum that they rust, but you can expose them to oxygen and over time see that they do indeed rust. Therefore, you know can state that iron is a metal capable of rusting (not all metals rust).

   The more properties we can identify for a substance, the better we know the nature of that substance.  These properties can then help us model the substance and thus understand how this substance will behave under various conditions.  The most useful properties are those which are quantitative and intensive because they do not require you to change the substance and they do not depend upon the amount of the sample you possess. However, classification is really more inferential since we are trying to make sense of our observations.

     On the simplest level, matter is that which is not energy.  Einstein proposed that the two were just extremes of each other and convertable through the equation of E=mc².  However, this relationship is anything but simple.  Energy, it seems, isn't made up of any one thing; instead, it's an abstract concept that is popularly defined as "the ability to do work".  But if you really want to force a breakdown of energy you could say, for example, that radiation comes in discrete clumps called photons. These can be thought of as making up radiative energy.  Similarly, interconversions between the bonds and structures of atoms and molecules can be thought of as giving rise to chemical energy.  Electrical energy depends on the movement of electrons.  Heat energy can be transmitted via radiation  conduction, or convection.  Conduction depends on molecules/atoms being close to each other and, similarly, convection relies on a interaction of atoms or molecules.  But the general classifications like Potential Energy (energy of position) and Kinetic Energy (energy of motion) can't really be broken down. 

    The conversion between matter and energy isn't anywhere near as simple as you would think because they're related on a fundamental level such that one is the other!  As it turns out, matter is every bit as abstract as energy and the ethereal energy that you hear about is as tangible as the matter you interact with!  At their core, the "particles" that make up everyday matter are really not anything like the solid spheres we all tend to imagine. And energy itself is a lot more ubiquitous and intrinsic part of our lives than we usually consider.  But what does the equivalence of matter and energy expressed by his famous equation E=mc², really mean?  It means that, at the fundamental level, there really is no difference between energy and matter. One is equivalent to the other. 

    So what does this mean to you?  It means that using this definition of matter is good for making gross generalizations, but that is as far as you can go.  This philosophical definition remains cerebral and useless in any real practical sense.  Another classification system is needed.

    Our most useful classification systems tend to be specific and conceptual (based on what we think are underlysing reasons). Conceptual definitions are preferred since distinguish types of matter and allow predictions based on characteristics.

   For example, reconsider the typical classification of states of matter, but now do so in terms of how the particles are arranged. A solid has slow moving particles due to strong interparticle attractions forcing the substance to maintain its shape and volume. A liquid, with its slightly faster moving particles has slightly weaker interparticle attractions allowing shape to vary and a gas with its extremely fast moving particles preventing any definite shape or volume since there are virtually no interparticle attractions.

    From this we can define other conditions of matter based on how the particles are arranged.

    Note that the difference between a solution and mixture depends upon the level of magnification and distribution of the particles.  Macroscopically solutions are very uniform while mixtures are not.  Microscopically solutions may not be as uniform as predicted, but this will not be detectable.  Mixtures demonstrate varying properties due to their macroscopic non-uniform distribution.
 

Solution	Mixture

    The more specific the classification system the more useful it becomes, but the more restrictive it becomes as well.  Thus the operational classification with properties such as density and solubility and colour tend to be most used in the laboratory, but require considerable work to explain on an atomic level. 

References

http://dept.physics.upenn.edu/courses/gladney/mathphys/subsubsection1_1_3_1.html
http://www.madsci.org/posts/archives/nov98/912178539.Ph.r.html
http://www.sickamongthepure.com/files/Graphics/Library/E_MC2.jpg
http://www.chem.tamu.edu/class/majors/tutorialnotefiles/intext.htm
http://chemsite.lsrhs.net/a_Intro/images/Overheads_large/classification_of_matter.jpg
http://www.edquest.ca/Notes/clofmat.jpg
http://itl.chem.ufl.edu/2045/matter/FG01_005.GIF
http://www.ilpi.com/msds/ref/gifs/statesofmatter.gif