Question about significant figures in a number?

Question

my chemistry teacher was very vague on what exactly the significant numbers are in a number. I'm just wondering how exactly you can tell which ones are and which ones are not. here are some examples of numbers I'm dealing with.

2.03

780

500,000,000

670,000.

0.800008

0.908

50

im just confused on the concept of significant figures and was hoping someone could explain it to me. of course whoever explains it best will get best answer 5*. =)

Answer 1

There's a pretty good guide on wikipedia. It'll show you how to do it.

Basically a 0 before a decimal point is not significant. If it's anywhere else, it is because it's acting as a place holder. 2.03 is 3 sig figs. 0.908 is also 3 sig figs. Every other non-zero number is also significant. If you have a number like 50, it's kind of ambiguous because it does not end with a decimal, so there may be error involved with it. This means that it may not be accurate to the nearest unit. The number 670000. has 6 sig figs and is perfectly fine because it ends with a decimal.

Answer 2

The are several factors used in determining which figures are significant and which are not. While I won't do your homework for you, I'll try my best to explain.

All non-zero digits are considered significant. (e.g. 25.9 has 3 sig. figs.)

Leading zeroes are NOT considered significant. (e.g. 0.0035 has 2 sig. figs.)

Zeroes appearing between two non-zero digits are significant (e.g. 2003.5 has 5 sig. figs.)

Trailing zeroes in a number containing decimal points are significant (e.g. 273.5200 has 7 sig. figs.)

The significance of trailing zeroes in a number without decimal points is ambiguous. For instance, your last example, 50 can have either two sig. figs. (5 and 0) or one sig. fig. (5). This depends on the device that was used to obtain the measurement. In a case where you simply have to state how many sig. figs. there are in a number, it is best to just find out from your teacher which (s)he prefers. Hope I helped.