How To Work Out Significant Figures
May 12th, 2006 by David Bradley >> 8 Comments
For anyone who hits the Significant Figures blog looking for an explanation of significant figures, you can find a quick cribsheet below or try out the significant figures calculator here.
Significant figures (sig figs or sf) are basically a way of expressing how accurately you measure something. It is a method of expressing error in measurement, in other words.
The most significant digit is the “first” digit of a number (the left-most digit). E.g. the most SF in the value 16.51 cm is that 1 in the “tens column, 6 is next, 0.5 , then 0.01. Thus, the least significant figure is the “last” digit of a number (the right-most digit). The further left you go in a number the more weight a value has, so that it’s more important to know that length is about 16 cm than to worry about the 0.01 cm (on most occasions).
So expressing 16.51 cm to two sig figs would be 17 cm, to three 16.5 cm and to four 16.51 cm.
The Significant Figures blog highlights the misuse of this system especially in the mainstream media. On the NASA site, one might see the average distance to the sun given as 149597870.691 km (1 astronomical unit, AU), for instance. This value is given to 12 significant figures, which is fine for NASA. But, most journalists would want a quick and easy number so it is usually rounded up to 150 million km (three sig digs). Problems arise, when those dudes next convert those modern km into the more traditional miles…and then give a value of 93.2 million miles, for instance.
This conversion somehow gains a sig fig in the conversion. BUT. SFs represent a measure of the error margins, the +/-, the give or take accuracy, so the conversion from km to miles has improved the accuracy of the value without actually physically determining this value with more precision. That’s just plain wrong. The only way to improve accuracy is to actually measure the distance more precisely (as NASA scientists have obviously done).
Anyway, I hope you get the point, check through the SF blog archives to find more examples of this kind of measurement nonsense.
Leave a comment ↓
Harmon // Feb 12, 2007 at 2:13 pm
Actually, 16.51 to two sig figs is 17! (Anything 5 or over rounds up.)
I teach sig figs in my Gen Chem class.
Mimi // Oct 7, 2007 at 5:25 pm
Very nice. I am delighted to have found somewhere with a straightforward explanation. As for Harmon’s reply, I think it depends on how you were taught..I was taught to round up, some were taught to round to an even number etc blah blah.
cc // Oct 28, 2008 at 9:30 pm
hi great advice but i’m trying to find one sig figure to 0.000364907 can anyone help me please?
David Bradley // Oct 28, 2008 at 9:49 pm
The sig figs calculator on this site will help, but what you are after is calculating your number *to* one sig fig, as opposed to trying to find one sig fig to your number…surely?
Math is diificult // Sep 13, 2009 at 12:42 pm
please help :
276479 to 3 sf
5215 to 3 sf
0.370794 to 3 sf
25624 to 2 sf
i need answers by this afternoon so plz help
David Bradley // Sep 14, 2009 at 10:26 am
I hope I’m too late. I certainly don’t want to do anyone’s homework for them. SFs are about rounding and discarding insignificant digits in a number, so to round the first one to 3 sf look at the biggest three parts of the number the “276″, i.e. the hundred thousands, the tens of thousands and the thousands. The fourth number is less than 5 so you can ignore it. Hence 276000. Carry on with exactly the same pattern. If the next digital along that you want to use sf is 5 or more then you round up the one to its left by one. So, 5215 to 3 sf, look at left three “521″ and the fourth is 5, so round up the 1 to its left and ignore it and any to the right: 5220 etc etc…
276479 to 3 sf is 276000
5215 to 3 sf is 5220
0.370794 to 3 sf 0.371
25624 to 2 sf is 26000
John // Jan 19, 2010 at 7:53 pm
when I want to divide 626.9 by 6, what would that be in significant digits?
Since 6 has only 1 significant diit, would it be just
100?
David Bradley // Jan 19, 2010 at 8:43 pm
If you’re working to 1 significant figure accuracy then, yes…