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.

Unit What it Measures
Meters Distance
Liters Volume
Grams Mass
Second Time
Kelvin Temperature

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.

### Fahrenheit, Celcius, and Kelvin

• 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.
• If you multiply the Celcius temperature by 9/5 (or 1.8) then add 32 it will give you the Fahrenheit temperature.
• Adding 273 to Celcius will give Kelvin, and subtracting 273 from Kelvin you will get Celcius.

The generic equations are as follows:

Example:

• (451oF - 32) / 1.8 = 233oC
• (20oC * 1.8) + 32 = 68oF
• 40oC + 273 = 313 Kelvin

Note: Kelvin does not have a degree mark nor is it said with a degree.

## Metric System Prefixes

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.

Metric System Prefixes
Prefix Mulitplied By Symbol
exa 1018 E
peta 1015 P
tera 1012 T
giga 109 G
mega 1000000 M
kilo 1000 k
hecto 100 h
deka 10 dk
deci .1 d
centi .01 c
milli .001 m
micro 10-6 µ
nano 10-9 n
pico 10-12 p
femto 10-15 f
atto 10-18 a

* If you are not using Netscape, the numbers that are after the 10 in the chart are superscripts

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)

Other Examples:

• 15cm = .15m
• 235kg = 235000g
• 12mm = 1.2cm
Metric System | Scientific Notation | Significant Figures | Dimensional Analysis | Top of Page

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 104. 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.

Scientific Notation Examples
Scientific Notation Regular Form
1.23 X 104 12300
4.91 X 103 4910
2.1 X 10-3 .0021

* If you are not using Netscape, the numbers that are after the 10 in the chart are superscripts

Metric System | Scientific Notation | Significant Figures | Dimensional Analysis | Top of Page

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:

• All non-zero numbers are significant.
• 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.
• 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.
• When the number has portions before and after the decimal then all the numbers are significant. Ex. 1700.023 has seven significant digits.
• 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.
• In Scientific Notation, significant digits are represented in the decimal number. Such as, 1.42 X 1012 has three significant digits because there are three numbers in the decimal number that is multiplied by 10 to some power.*

* If you are not using Netscape, the numbers that are after the 10 in scientific notation are superscripts

The rules for determining the number of significant digits after a calculation are grouped by Addition and Subtaction, and Multipication and Division.

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.

Example:

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.

### Multiplication and Division

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.

Example:

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.

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.

Metric System | Scientific Notation | Significant Figures | Dimensional Analysis | Top of Page

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.
In Dimensional analysis you can setup the equation like this.

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.

Other Examples:

13.1 g (1000mg / 1g) = 13,100 mg

Metric System | Scientific Notation | Significant Figures | Dimensional Analysis | Top of Page