# Rounding off numbers

1. May 29, 2014

### Maxo

Let's say we have a result with the number 2624,499 and want to round it off to a certain number of significant figures.

Some examples with different number of significant figures:

a) 3 significant figures:

2420 or 2430?

b) 4 significant figures:

2624 or 2625?

c) 5 significant figures:

2624,4 or 2624,5?

The question is about the fours, should one think that the 4 to the right is rounded off upwards to 5 because of the nines and then this 5 will round off the left 4 upwards to 5? Or should you simply "cut off" all significant figures after the ones you want to include?

2. May 29, 2014

### Staff: Mentor

Neither.

Former.

Latter.

3. May 29, 2014

### Maxo

Why? What would you round it off to? Would it rather be 2,62*10^3 then?

It seems here you are using the principle, that one should look at one extra significant digit above the number of significant digits you want, and if that digit is 5 or more, the last significant digit should be rounded off upwards, otherwise not. Any extra digits that are two steps or more to the right of the number significant digits you want should be ignored though. Is that correct?

4. May 29, 2014

### D H

Staff Emeritus
Or 2620. You wrote 2420 in the opening post.

5. May 29, 2014

### Staff: Mentor

Yes.

Note that consecutive rounding (which seem to be behind your question) are a sure way of introducing errors larger than necessary.

If 0.449 is rounded directly to 0.4, you introduce error of 0.049.
If 0.449 is rounded to 0.45 first and then to 0.5, you introduce error of 0.051.
You want the rounding error to be as small as possible, so the first strategy is obviously better.

Note that in the case when the last digit is exactly 5 there are many different rounding strategies. There is a long article listing them in wikipedia.