You can see that you can't be sure whether it's 6.1489898 or 6.1501239223. The rule for this is; get as many numbers you can be sure of, and then make an educated guess about the last digit. So in this example, you can see it's definitely between 6 and 7, so you know for sure the first number is 6. You can also see it's between the .1 and .2 marks, so you know it's 6.1 for sure. But the next, and last digit is uncertain. It looks like the end lies just around halfway between .1 and .2, so a safe guess is .05. Your final measurement should be around 6.15, of which all numbers are significant figures.
(Note: If you need more examples, tell me. I don't know if some people need this reinforced or something, that's all I plan to include on this.)
You'll need to know how many sig figs are in a measurement, to make proper calculations. Here are some guidelines.

When you do your calculations, you might naturally be tempted to write as many numbers down as your calculator feeds, thinking that it is more accurate. WRONG! Your accuracy of your answer can only be as precise as the numbers the problems give you! For example, if a problem says something like this:
3.0 liters of water is added to 3.14159265358979323 liters of water. How many liters of water are there?
The answer is not 6.14159265358979323. 3.0 liters means that the actual value could be anywhere from 2.9 to 3.1 liters (remember the last number is just a guess?). So with that much uncertainty, going all the way down to 3 x 1012 liters doesn't have as much an effect as the +/0.5 that you have. The correct answer is 6.1 liters. How? Here are a few simple rules governing the realm of sig figs:
 To multiply or divide: You find the number with the least sig figs, and use that many sig figs in the answer.
 To add or subtract: The last digit in the final answer must have the same place as the place of the least precise number. That is, the leftmost ending value.
That's all there is to it. And just in case you forgot how to round (something you should've learned in like fifth grade...)
 Remember to finish all your addings and multiplyings, then round.
 If the number to the right of where you're rounding to is 4 or less, leave it alone and kill the numbers to right of it.
 If the number to the right of where you're rounding to is 5 or greater, add one to the number and kill the numbers to right of it.
Instead of the annoying British system, with its gallons and quarts and pints and who knows what, the SI system has an easier way of remembering how many small units go into one big unit. It's the prefix system, and it's based on powers of ten. Makes it very simple. Here is a table on some of the most commonly used prefixes:

So, some quick examples are: one kilometer is a thousand meters; one dekagram is a hundred decigrams, and you can go on from there. These are only the most used prefixes; other ones aren't used much in chem. Anyway, a more extensive list of prefixes will be included later in the reference area.
Dimensional Analysis
Note a few things. First, to convert you multiply your starting point with a series of fractions to get the final answer. Each fraction is a unit over another, which are equal. In the example, 100 cm is equal to 1 m, and 1 inch is equal to 2.54 cm. Thus multiplying by one. The trick to figuring out what to put in each fraction is looking at the units in the top of the previous fraction, and putting that unit in the bottom of the next one. You look at meters in the top of the first fraction (it's 100. meters / 1), and put that in the bottom of the next one. To figure out what unit to put in top, you look at the final answer, and see if you can get a direct relation to it. Most people don't know directly how many inches are in a meter, but it is common knowledge that there are 2.54 cm in an inch. So perhaps converting into centimeters is a start...
Once you get the units right, plug in the numbers that make the top equal the bottom. You should know that 100 cm's is an m. Now you go to the next fraction. cm's go in the bottom, and you can go straight to inches, knowing the relation. You ultimately wants the units converting to in the top of the last fraction. That way, everything cancels out, and you're done.
Plugging the values in, and multiplying the fractions give you the answer.
Another couple of examples:
Converting 3.450 kg's into pounds.
Converting 434.2 atm's into torr:
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Usage of Periodic Table
You will be using the periodic table until your head explodes, so you'd better learn to use it quick and efficiently from the beginning onward. I made a cool periodic table image map that lets you click on an element, and gives info on it. Here is a section of it, and what the number means.
Atomic Number: This is how many protons are in the nucleus of one atom of this element. It also shows the number of electrons in a stable atom of this element.
Symbol : This is the shorthand way of writing the element, and you will see it like this in chemical equations.
Atomic Mass : This is the number you will be using the most during the AP test. It is how much one atom weighs, in amus. 1 amu is 1 gram divided by Avogadro's number (6.022 x 10^{23}). So in other words, one mole of beryllium has a mass of 9.012 grams. Anytime you need a molecular mass, you will be adding multiples of atomic masses. Memorize some of the most common ones; it will save you some lookingup time.
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Chemistry Basics (Part 1)
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