significant figures?

Question

how do you know how many significant figures there are for a number like what are the rules...oh and like when do you use cientific notation with sig figs and when dont you....EXAMPLES PLEASE!

Answer 1

Significant figures are only used with measured numbers. All non-zeros in a measured number are significant. All zeros between non-zeros are significant. ex: 502 = 3 S.F. All zeros that are to the right of a non-zero number with a decimal point in the number are significant. ex: 13.00 = 4 S.F.
You can use scientific notation with all of the numbers, but if the number is like 500 and there are only 2 S. F., then you write as 5.0 x 10^2, to show that there are 2 not 1 S.F.

Answer 2

Only by using scientific notation can you tell from the number how many significant figures it has. For example, if I give you the number 36000, it is not clear if that number has 5 significant figures or less. It could have been 35998 rounded up, However if I express that number as

3.6 * 10^4, that clearly means two significant figures;
3.60 *10^4 means 3 significant figures;
3.600 * 10^4 means 4 significant figures.

Specifically, 3.600 * 10^4 means the number is >3.5995 and <3.6005.