Significant digit

Well, for example, if you measure the radius of a circle as 4.1m with a ruler. You also measure the speed of an object moving along the circle as 5.2m/s using a meter wheel and a stopwatch. Now, you also measure the mass of the object with a highly accurate, calibrated scale, and this gives you a mass of 3.456789kg.

Now in working out the centripetal force we put in the numbers and get an answer as 22.797945N

However, are we justified in quoting it to that many significant figures? No, because our speed and radius measurements were only accurate to 2 sig figs, so this means that our answer can only really be meaningful to 2 sig figs. So a better answer would be to say the force is 23N, because that lets other people know when they read your work, that you're accurate to 2 sig figs. All the effort that you put into measuring the mass accurately is meaningless because you're multiplying it by innaccurate measurements which have a higher error associated with it. If you quoted your answer as 22.797945N, you would be giving the false impression that your measurements were more accurate than they were.

For instance you speed would be +/- 0.05 m/s ans your radius would be +/- 0.05, but your mass measurement is +/- 0.0000005, but this is completely negligible compared to the error in your other measurements, so you have to let them take precident.

I think you have the wrong idea upon reading what you wrote Jerry. By quoting to only 2 sig figs in this case, you are being more accurate. You are just being less precise - which is fine if some of your measurements aren't precise (they're still accurate!).

You should look up the difference between precision and accuracy. Accuracy is important - precision is less important but nice if you can get it.

Oh, ok! I get it better. Thanks Cap!

7 for my 10p worth!