# Significant Figure Rounding

• Jul 30th 2012, 08:38 AM
Chaim
Significant Figure Rounding
I kind of understand Significant Figures, but I was having a tough time rounding.
For example, if we have 0.732 m, the significant figures is 3.
If we were to round it to 2 significant figures, then the answer would be 0.73 m

Just like 142,000 g has three significant figures
If we were to round it to 2 significant figures, then the answer would be 140,000 g

Another example is 5.23 * 103 km, which has three significant figures
If we were to round it to 2 significant figures, then the answer would be 5.2 * 103 km

But I'm kind of confuse on how to round something like 1050 in.
Since 1050 has 4 significant figures, then how would I make it into 2?
Since this isn't like decimals anymore, and if I get rid of the last 2 digits, 5 and 0, it will make it into 1000, which would make it only have 1 significant figure.

Can anyone explain it to me?
Thanks
• Jul 30th 2012, 09:11 AM
emakarov
Re: Significant Figure Rounding
Read this section of the Wikipedia article about significant figures. When there are trailing zeros and no decimal point, the number of significant figures has to be specified explicitly. Thus, 1050 may have 3 or 4 s.f., and 1000 may have 1 to 4 s.f. The result of rounding of 1050 to 2 s.f. is 1000 to 2 s.f.

Edit: Rather, the result of rounding of 1050 to 2 s.f. is 1100 to 2 s.f. if the round half up tie-breaking rule is used.
• Jul 31st 2012, 07:27 AM
Chaim
Re: Significant Figure Rounding
Ah ok thanks!
• Jul 31st 2012, 08:30 AM
HallsofIvy
Re: Significant Figure Rounding
There are two commonly used conventions for rounding if the first digit removed is 5:
1) Always round up. The reasoning here is that the digits after the 5 will make the actual number closer to the next place up.
2) Always round to the closest even number. There is nothing special about "even"- the reasoning here is that we are "halfway" between two digits and, since the previous digit will be even about half the time, this will result in rounding "up" half the time and rounding "down" half the time.