Most pieces of information are not truly accurate, most are usually assumptions, or were made with not very precise equipment. Most good figures have a lot of decimal places(1.234543535, or whatever), but precise information should come from precise data, if it doesn�t, then that information isn�t really precise isn�t it.

For example, you wanted to find out the density of a lump of aluminum. Now the formula for density is Mass/Volume, so to get volume you accurately place it in a cylinder with some water, and find the volume to be 334 mL, but to get the mass you just weigh the lump in your hands, and feel that it�s about one kilogram (1,000 grams).

but you just weighed the rock with your hands, how can you use a number of 2.99401198 if you used inaccurate information to begin with?

In case of these situations, scientists have developed rules for using certain amounts of digits. First, how important are these types of digits? How significant are they? well here�s some rules to determine significant digits (or sig figs for short):

All non zeros are significant All "trapped" zeros are significant Trailing zeros after a decimal are significant Zeros and other numbers used in scientific notation are significant ther zeros are not significant

Examples:

• The number 238 has three sig figs because each of the three numbers isn�t a zero.
• The number 208 would also have three sig figs because the zero in the middle is "trapped" between the 2 and the 8.
• The number 280 would have only two sig figs because it only has the 2 and the 8, the last zero isn�t trapped.
• The number 28,000.5 would have six sig figs because it has the 2, the 8, and the 5 at the end along with the three 0�s that�s "trapped".
• The number .007 would have three sig figs
• The number 1.00 x 10³ would have three sig figs because the zeros are in scientific notation

O.K., now what about the 3rd rule, what do you mean by "trailing zeros"? Well, what if you have a measurement that is exactly 6 or exactly 3? It would really be 6.000000000 or 3.000000000, the zeros going on to infinity because the measurement was exactly accurate. You usually get things as accurate in given things. For example when there is exactly 24 hours in a day, 24 is going to have infinite sig figs. Also there is exactly 100 pennies on the dollar, that�s 100.0000000000000000 pennies, so it also has an infinite amount of sig figs.

So here�s another important rule in chemistry. Your result should have the same amount of sig figs as the piece of data with the least amount of sig figs, or basically, the "worst" piece of data. For example, remember when the density of that lump of aluminum was calculated above? The "worst" piece of data was the mass of the rock; it was weighed to be 1,000 grams. 1,000 has one sig fig, so the resulting density, 2.99401198 g/mL, should also have one sig fig, so rounding it to one sig fig it�s 3 g/mL. You should always carry out your calculations entirely before rounding.

When you make measurements in chemistry you will never find a scale so accurate that is measures a lump a metal to be 34.098873794729737874937 grams, and nothing will be exactly 34.000000000000 grams, yet when you put all you calculations in your calculator you always get a number like 23.9776509872109 with a whole bunch of decimal places. These rules of sig figs are used to tell you how many decimal places to round to.

There is one important exception to this rule. On the A.P. Chemistry test issued by the college board, the rule is to use only three sig figs in all your calculations. This is to help stop confusion on a shortly timed test. Some chemists also use just three sig figs, but most follow the rule above by using the "worst" piece of information, and your teacher should probably do so as well.