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<h1><!--mstheme--><font color="#000099"><img src="../../media/mathrev/mathtitle.gif" alt="mathtitle.gif" width="283" height="42"><!--mstheme--></font></h1>
</center>
<ol>
<li><a href="#metric">Metric System</a>
<li><a href="#scinot">Scientific Notation</a>
<li><a href="#figues">Significant Figures</a>
<li><a href="#da">Dimensional Analysis</a>
</ol>
<!--msthemeseparator--><p align="center"><img src="../../../../_themes/education/blrule.gif" width="600" height="10"></p>
<a name="metric"></a>
<img src="../../media/mathrev/ruler.jpg" width="100%" alt="ruler.jpg">
<center>
<h2><!--mstheme--><font color="#0033CC">Metric System<!--mstheme--></font></h2>
</center>
<p>The Metric System is the most commonly used mesurement system in the
world and in the scientific community. The metric system uses the units in
the chart for measurement.</p>
<!--mstheme--></font><table border=5 cellspacing=4 bordercolordark="#000000" bordercolorlight="#000000" >
<tr>
<th><!--mstheme-->Unit<!--mstheme--></font></th>
<th><!--mstheme-->What it Measures<!--mstheme--></font></th>
</tr>
<tr>
<td><!--mstheme-->Meters<!--mstheme--></font></td>
<td><!--mstheme-->Distance<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->Liters<!--mstheme--></font></td>
<td><!--mstheme-->Volume<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->Grams<!--mstheme--></font></td>
<td><!--mstheme-->Mass<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->Second<!--mstheme--></font></td>
<td><!--mstheme-->Time<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->Kelvin<!--mstheme--></font></td>
<td><!--mstheme-->Temperature<!--mstheme--></font></td>
</tr>
</table><!--mstheme-->
<p>Kelvin? What's that you say? Kelvin is the unit that is used in most
calculations in Chemistry. Celcius is also often used because of its easy
conversion to and from Kelvin. Fahrenheit is the most common scale in the
U.S., so converting among all three is necesssary.
<p><h3><!--mstheme--><font color="#6666CC">Fahrenheit, Celcius, and Kelvin<!--mstheme--></font></h3>
<!--mstheme--></font><!--msthemelist--><table border="0" cellpadding="0" cellspacing="0" width="100%">
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->If you subtract 32 from the Fahrenheit temperature and multiply by
5/9 (or divide by 1.8) then it will convert to Celcius temperature.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->If you multiply the Celcius temperature by 9/5 (or 1.8) then add
32 it will give you the Fahrenheit temperature.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->Adding 273 to Celcius will give Kelvin, and subtracting 273 from Kelvin
you will get Celcius.
<!--msthemelist--></table><!--mstheme-->
<p>The generic equations are as follows:
<center>
<img src="../../media/mathrev/f_c_eq.gif" alt="Generic Equations" width="306" height="213">
</center>
<p>Example:
<!--mstheme--></font><!--msthemelist--><table border="0" cellpadding="0" cellspacing="0" width="100%">
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->(451<sup>o</sup>F - 32) / 1.8 = 233<sup>o</sup>C
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->(20<sup>o</sup>C * 1.8) + 32 = 68<sup>o</sup>F
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->40<sup>o</sup>C + 273 = 313 Kelvin
<!--msthemelist--></table><!--mstheme-->
<p><i>Note:</i> Kelvin does not have a degree mark nor is it said with a
degree.
<center><h2><!--mstheme--><font color="#0033CC">Metric System Prefixes<!--mstheme--></font></h2></center>
<p>One of the many reasons the metric system is used is for its easy
ability to add prefixes that change the value of the unit. For example: the
prefix kilo- on grams means that 1000 grams equals 1 kilogram. In the
example the prefix mulitiplied the original unit's value by 1000 because
that is what kilo- stands for. The chart shows the most used prefixes in
italics and the least used in regular print. This chart can be used to
find the prefix of whatever unit you are working with.</p>
<!--mstheme--></font><table border=5 cellspacing=4 bordercolordark="#000000" bordercolorlight="#000000">
<caption>Metric System Prefixes</caption>
<tr>
<th><!--mstheme-->Prefix<!--mstheme--></font></th>
<th><!--mstheme-->Mulitplied By<!--mstheme--></font></th>
<th><!--mstheme-->Symbol<!--mstheme--></font></th>
</tr>
<tr>
<td><!--mstheme-->exa<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>18</sup>
<td><!--mstheme-->E<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->peta<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>15</sup><!--mstheme--></font></td>
<td><!--mstheme-->P<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->tera<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>12</sup><!--mstheme--></font></td>
<td><!--mstheme-->T<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->giga<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>9</sup><!--mstheme--></font></td>
<td><!--mstheme-->G<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme--><i>mega</i><!--mstheme--></font></td>
<td><!--mstheme-->1000000<!--mstheme--></font></td>
<td><!--mstheme-->M<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme--><i>kilo</i><!--mstheme--></font></td>
<td><!--mstheme-->1000<!--mstheme--></font></td>
<td><!--mstheme-->k<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->hecto<!--mstheme--></font></td>
<td><!--mstheme-->100<!--mstheme--></font></td>
<td><!--mstheme-->h<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->deka<!--mstheme--></font></td>
<td><!--mstheme-->10<!--mstheme--></font></td>
<td><!--mstheme-->dk<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme--><i>deci</i><!--mstheme--></font></td>
<td><!--mstheme-->.1<!--mstheme--></font></td>
<td><!--mstheme-->d<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme--><i>centi</i><!--mstheme--></font></td>
<td><!--mstheme-->.01<!--mstheme--></font></td>
<td><!--mstheme-->c<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme--><i>milli</i><!--mstheme--></font></td>
<td><!--mstheme-->.001<!--mstheme--></font></td>
<td><!--mstheme-->m<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme--><i>micro</i><!--mstheme--></font></td>
<td><!--mstheme-->10<sup>-6</sup>
<td><!--mstheme-->µ<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->nano<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>-9</sup><!--mstheme--></font></td>
<td><!--mstheme-->n<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->pico<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>-12</sup><!--mstheme--></font></td>
<td><!--mstheme-->p<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->femto<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>-15</sup><!--mstheme--></font></td>
<td><!--mstheme-->f<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->atto<!--mstheme--></font></td>
<td><!--mstheme-->10<sup>-18</sup><!--mstheme--></font></td>
<td><!--mstheme-->a<!--mstheme--></font></td>
</tr>
</table><!--mstheme-->
<p><cite>* If you are not using Netscape, the numbers that are after
the 10 in the chart are superscripts</cite></p>
<p>If you wanted to know how many meters are in 4 megameters the conversion
chart could be consulted. You would discover that 1 megameter = 1000000
meters. So 4 * 1000000 = 4000000. Therefore 4 megameters = 4000000
meters. (This can also be accomplished by moving the decimal six places)
<p>Other Examples:
<!--mstheme--></font><!--msthemelist--><table border="0" cellpadding="0" cellspacing="0" width="100%">
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->15cm = .15m
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->235kg = 235000g
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->12mm = 1.2cm
<!--msthemelist--></table><!--mstheme-->
<!--msthemeseparator--><p align="center"><img src="../../../../_themes/education/blrule.gif" width="600" height="10"></p>
<center>
<a href="#metric">Metric System</a> |
<a href="#scinot">Scientific Notation</a> |
<a href="#figues">Significant Figures</a> |
<a href="#da">Dimensional Analysis</a> |
<a href="#top">Top of Page</a><br>
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<h2><!--mstheme--><font color="#0033CC">Scientific Notation<!--mstheme--></font></h2>
</center>
<p>Scientific Notation is a way to abbreviate very large or very small numbers.
The format of Scientific Notation is this: a number that has a decimal after
the first digit, mulitiplied by ten with an exponent. An example is:
1.23 X 10<sup>4</sup>. The exponent can be positive or negative. If
the exponent is positive then you move the decimal to the right by the
number of the exponent. If the exponent is negative then you move the
decimal to the left by the number of the exponent. This form of numbers
can express very large and small numbers depending on the exponent.
More examples are as follows.<br></p>
<!--mstheme--></font><table border=5 cellspacing=4 bordercolordark="#000000" bordercolorlight="#000000">
<caption>Scientific Notation Examples</caption>
<tr>
<th><!--mstheme-->Scientific Notation<!--mstheme--></font></th>
<th><!--mstheme-->Regular Form<!--mstheme--></font></th>
</tr>
<tr>
<td><!--mstheme-->1.23 X 10<sup>4</sup><!--mstheme--></font></td>
<td><!--mstheme-->12300<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->4.91 X 10<sup>3</sup><!--mstheme--></font></td>
<td><!--mstheme-->4910<!--mstheme--></font></td>
</tr>
<tr>
<td><!--mstheme-->2.1 X 10<sup>-3</sup><!--mstheme--></font></td>
<td><!--mstheme-->.0021<!--mstheme--></font></td>
</tr>
</table><!--mstheme-->
<p><cite>* If you are not using Netscape, the numbers that are after the
10 in the chart are superscripts</cite></p>
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<a href="#scinot">Scientific Notation</a> |
<a href="#figues">Significant Figures</a> |
<a href="#da">Dimensional Analysis</a> |
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<h2><!--mstheme--><font color="#0033CC">Significant Figures<!--mstheme--></font></h2>
</center>
<p>Significant Figures or Digits are the amount of digits that are accurate
in a calculation. This is determined by how many digits there are in
the numbers of the calculation. The rules for determing how many significant
digits are as follows:<br>
<!--mstheme--></font><!--msthemelist--><table border="0" cellpadding="0" cellspacing="0" width="100%">
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->All non-zero numbers are significant.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->Zeroes at the end of a number that has no decimal point are not
significant. Ex. 500 only has one significant digit because the
zeroes after the five do not count.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->If a decimal point is placed after the last zero the zeroes do count as
significant digits. Ex. 500. has three significant digits because the
decimal point makes the zeroes significant.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->When the number has portions before and after the decimal then all the
numbers are significant. Ex. 1700.023 has seven significant digits.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->In numbers that only have a decimal portion, zeroes at the beginning of
the number do not count as significant. Ex. .00254 has three significant
digits because the zeroes at the beginging of the number do not count.
<!--msthemelist--><tr><td valign="baseline" width="42"><img src="../../../../_themes/education/blbull1.gif" width="15" height="15" hspace="13"></td><td valign="top" width="100%"><!--mstheme-->In Scientific Notation, significant digits are represented in the
decimal number. Such as, 1.42 X 10<sup>12</sup> has three significant
digits because there are three numbers in the decimal number that is
multiplied by 10 to some power.*
<!--msthemelist--></table><!--mstheme-->
<p><cite>* If you are not using Netscape, the numbers that are after the 10
in scientific notation are superscripts</cite></p>
<p>The rules for determining the number of significant digits after a calculation
are grouped by Addition and Subtaction, and Multipication and Division.
<p><br><h3><!--mstheme--><font color="#6666CC">Addtion and Subtraction<!--mstheme--></font></h3></p>
<p>When two or more numbers are added or subtracted the final answer is
rounded off to the same decimal place as the number having its last significant digit
the furthest to the left.
<p>Example:
<p>If you have the numbers 4.501 and 90.2 added together you will
get 94.7 because the last column that both numbers use is the tenths place.</p>
<p><br><h3><!--mstheme--><font color="#6666CC">Multiplication and Division<!--mstheme--></font></h3></p>
<p>Significant digits in Multipication and Division are determined by the
number of significant
digits in each of the numbers in the calculation. The answer must have
the same amount of
significant digits as the number in the calculation with the least amount
of significant
digits.
<p>Example:
<p>If you multiply the numbers 500 and 256 together the
answer would be
100000 because 500 only has one significant digit so the answer can have only
one significant
digit.</p>
<p>If you divide 1575 (four significant figures) by 17.6 (three significant
figures), you round your answer to 89.5 (from 89.48863) so that it will
have 3 significant digits.
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<center>
<a href="#metric">Metric System</a> |
<a href="#scinot">Scientific Notation</a> |
<a href="#figues">Significant Figures</a> |
<a href="#da">Dimensional Analysis</a> |
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<center>
<h2><!--mstheme--><font color="#0033CC">Dimensional analysis<!--mstheme--></font></h2>
</center>
<p>Dimensional analysis is a process that allows changing of units. If you
were going to change from centimeters to meters Dimensional analysis allows
an easy way to change. To start you must decide what the conversion
factor is, so we know that 100 centimeters = 1 meter.<br>
In Dimensional analysis you can setup the equation like this.<br><br>
<center>
<img src="../../media/mathrev/eq1.gif" alt="Equations Examples" width="230" height="31">
</center>
<p>The centimeters are in the denominator of the conversion factor because
the measurement is already in centimeters. The answer comes
out in meters because the centimeters cancel in the division.
<p>Other Examples:
<p>13.1 g (1000mg / 1g) = 13,100 mg <br>
<p><img src="../../media/mathrev/da_ex_1.gif" alt="hours to seconds" width="366" height="69">
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