# Rules for rounding numbers **URL:** \ **Category:** Factual Questions\ **Created:** [June 17, 2003, 10:10pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558 "2003-06-17T22:10:29Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 17, 2003, 10:10pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/1 "2003-06-17T22:10:29Z")
Say I have the following number and want to round it to two decimal places: 1.3249 Does the 9 round the 4 up to a 5 so the answer is 1.33 or do you just use the ‘4’ (ignore the 9) so the answer is 1.32? ---
**Author:** ![MC\_Master\_of\_Ceremonies](https://avatars.discourse-cdn.com/v4/letter/m/bb73d2/32.png) [@MC\_Master\_of\_Ceremonies](https://boards.straightdope.com/u/MC_Master_of_Ceremonies)\ **Post date:** [June 17, 2003, 10:14pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/2 "2003-06-17T22:14:00Z")
No you only use the digit after the decimal palce you want to round up to, so it rounds up to 1.32. ---
**Author:** ![hobbes730](https://avatars.discourse-cdn.com/v4/letter/h/97f17d/32.png) [@hobbes730](https://boards.straightdope.com/u/hobbes730)\ **Post date:** [June 17, 2003, 10:15pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/3 "2003-06-17T22:15:33Z")
You wording is a bit confusing MC; you round _down_ to 1.32 🙂 ---
**Author:** ![MaceMan](https://avatars.discourse-cdn.com/v4/letter/m/4bbf92/32.png) [@MaceMan](https://boards.straightdope.com/u/MaceMan)\ **Post date:** [June 17, 2003, 10:17pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/4 "2003-06-17T22:17:53Z")
Ignore the number after the 4. Think of it this way: 49 is less than 50, so you should always round down. Now, if the number had been 1.3250, the common convention is to round to the nearest even digit—therefore, you’d round down half the time and up all other times. In this case, you’d get 1.325—\>1.32 if the number had been 1.335, you’d round up to 1.34. Easy, right? ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 17, 2003, 10:23pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/5 "2003-06-17T22:23:56Z")
> [@](#): > > \*Originally posted by MaceMan \* > \*\*…the common convention is to round to the nearest even digit—therefore, you’d round down half the time and up all other times. In this case, you’d get 1.325—\>1.32 if the number had been 1.335, you’d round up to 1.34. Easy, right? \*\* Wow…I never knew that. I was always of the feeling that always rounding up with a ‘5’ was a little lopsided and the method you describe seems to level the field. Still…I swear I had never heard that before. Is this a relatively new convention? One only used in certain instances like (say) financial sheets or did my education fail me in this regard? ---
**Author:** ![MC\_Master\_of\_Ceremonies](https://avatars.discourse-cdn.com/v4/letter/m/bb73d2/32.png) [@MC\_Master\_of\_Ceremonies](https://boards.straightdope.com/u/MC_Master_of_Ceremonies)\ **Post date:** [June 17, 2003, 10:27pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/6 "2003-06-17T22:27:50Z")
I’ve never heard of the convention of rounding up to the nearest even digit. At college and uni doing Physics alot of my early course were about calculating experimental error so are you sure it’s not only a convention in afield like statistics where it would have an advantage? ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [June 17, 2003, 10:41pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/7 "2003-06-17T22:41:54Z")
I believe that rounding to even on .5 is called ‘bank rounding’ and there’s quite an argument for it being the ‘fairest’ method. ---
**Author:** ![MaceMan](https://avatars.discourse-cdn.com/v4/letter/m/4bbf92/32.png) [@MaceMan](https://boards.straightdope.com/u/MaceMan)\ **Post date:** [June 17, 2003, 11:03pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/8 "2003-06-17T23:03:44Z")
This convention has been around for ages…all my college chemistry classes used it, and I think I was taught it in grade school too. That being said, I did have one professor who said “just round up on a 5”, and I know a lot of scientists who do this, even though it is not really the best way to round. The reason why one should round down half the time, and up the other times is simple: picture a number line from 0 to 1, and then draw a line at 0.5—which is closer, O or 1? 🆒 One further clarification…the rule for rounding to the nearest even digit is only when that number ends in 5 (or 5 followed by some number of zeros) So, if the number had been 1.32501, you would round up to 1.33, because 501 is larger then 500. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [June 17, 2003, 11:19pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/9 "2003-06-17T23:19:22Z")
Computers sometimes do odd and unexpected things with rounding too due to the way that floating-point numbers are internally represented. ---
**Author:** ![stoyel](https://avatars.discourse-cdn.com/v4/letter/s/54ee81/32.png) [@stoyel](https://boards.straightdope.com/u/stoyel)\ **Post date:** [June 17, 2003, 11:37pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/10 "2003-06-17T23:37:09Z")
If you round up on .5, then in five of ten cases you will round down: 0 1 2 3 4 and in five of ten cases you will round up: 5 6 7 8 9 Rounding to the nearest even number strikes me as really bizarre, somehow. But maybe I’m just dense. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [June 17, 2003, 11:43pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/11 "2003-06-17T23:43:18Z")
Is case 0 _really_ rounding down? 5.1230 \> 5.123 is neither up nor down. ---
**Author:** ![Bippy\_the\_Beardless](https://avatars.discourse-cdn.com/v4/letter/b/ac8455/32.png) [@Bippy\_the\_Beardless](https://boards.straightdope.com/u/Bippy_the_Beardless)\ **Post date:** [June 17, 2003, 11:46pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/12 "2003-06-17T23:46:13Z")
**MaceMan** I think the rounding to even on .5 is more important for this reason. When you have a value rounded multiple times: Eg. 0.4449 if we round up on a 5 we get 0.4449 to 3dp = 0.445 0.445 to 2dp = 0.45 0.45 to 1 dp = 0.5 0.5 to 0 dp = 1 if we round to even on a 5 we get 0.4449 to 3dp = 0.445 0.445 to 2dp = 0.44 0.44 to 1 dp = 0.4 0.5 to 0 dp = 0 this sort of multiple roundings can very easily be introduced into a computer financial program by accident, and only rounding to even (specifically not rounding 0.45 to 0.5) avoids the passing on of a worsening error that would cause 0.4449 to round up to 1 by mistake. ---
**Author:** ![stoyel](https://avatars.discourse-cdn.com/v4/letter/s/54ee81/32.png) [@stoyel](https://boards.straightdope.com/u/stoyel)\ **Post date:** [June 17, 2003, 11:51pm UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/13 "2003-06-17T23:51:28Z")
Yes, case 0 is rounding down. If you round 3.00000001 to the nearest integer, you’re still rounding down. Everything else is haggling over sigfigs. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [June 18, 2003, 1:55am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/14 "2003-06-18T01:55:30Z")
Assuming that what the OP wants to do is to round 1.3249 to the **nearest hundredth** , it would be 1.32, because 1.3249 is (slightly) closer to 1.32 than it is to 1.33. If you were rounding 1.3251 (or 1.325anything, with any digit(s) after the five) to the nearest hundredth, it would be 1.33, since 1.32 is closer to 1.33 than it is to 1.32 (1.325 exactly would be the halfway point between 1.32 and 1.33, and 1.3251 \> 1.325). If you were rounding 1.325 to the nearest hundredth, well, 1.32 and 1.33 are equally near, so neither would be exactly wrong. Some people use the convention to always round to an even digit in the interest of fairness; some people always take the 5 to mean “round up” even if there aren’t any more digits after it, in the interest of simplifying the rounding rule. Of course, the right way to round depends on context. In some situations, you might _always_ want to round _up_ to the next highest, or down to the next lowest, whole number. ---
**Author:** ![spinky](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@spinky](https://boards.straightdope.com/u/spinky)\ **Post date:** [June 18, 2003, 2:12am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/15 "2003-06-18T02:12:16Z")
**Mangetout** , consider the amount the value changes: ```auto if the digit is the rounding changes the value by: --------------------------------------------------------------- 0 0 1 -1 2 -2 3 -3 4 -4 5 +5 6 +4 7 +3 8 +2 9 +1 ``` So you can see that the number decreases 4 times out of 10, increases 5 times out of 10, and stays the same 1 out of 10 times. That’s why “round up for 5” is lopsided. ---
**Author:** ![spinky](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@spinky](https://boards.straightdope.com/u/spinky)\ **Post date:** [June 18, 2003, 2:13am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/16 "2003-06-18T02:13:21Z")
Sorry, I meant to direct that last comment to **stoyel**. ---
**Author:** ![stoyel](https://avatars.discourse-cdn.com/v4/letter/s/54ee81/32.png) [@stoyel](https://boards.straightdope.com/u/stoyel)\ **Post date:** [June 18, 2003, 2:21am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/17 "2003-06-18T02:21:11Z")
I’m still not clear where fairness enters into it. If you’re doing measurements so delicate that having the last digit slightly off is a problem, use an extra digit. My science teachers in high school were consistent about this (and my profs in college have yet to express an opinion); you should keep one digit beyond what your instrumentation can measure precisely. Seems reasonable to me – if your balance is accurate to one tenth of a gram, then read the scale at one hundredth; you can usually tell whether it’s closer to 1.8 or 1.9, so call it 1.87 for later reference, even if you can’t be sure whether it was really 1.86 or 1.88. You just know it was somewhere on the high side. Of course, your results should be rounded properly, so as not to imply that your instruments are more precise than they actually are, but why do it before you have to? And if it’s an issue of converting fractions into imprecise decimals (as in finance), then what are you doing moving to decimals before you’re done, you silly schmuck? 😉 Statistically, rounding to the nearest even number may be more ‘fair’, but I can’t think of a situation where it would be better to rely on that random chance than to just keep track of one more digit for a little while. I maintain that case 0 is just as valid a case as any other, and rounding up at .5 isn’t lopsided at all – and if we’re going by statistics here, it’s infinitely unlikely to get an answer of precisely 3.0 assuming all possible values between 3.0 and 3.1 are equally likely. If you’re absolutely sure it’s 3.5 and not 3.49999999 or 3.50000001, you don’t need to round at all. ---
**Author:** ![stoyel](https://avatars.discourse-cdn.com/v4/letter/s/54ee81/32.png) [@stoyel](https://boards.straightdope.com/u/stoyel)\ **Post date:** [June 18, 2003, 2:24am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/18 "2003-06-18T02:24:22Z")
Oh, sure, reply while I’m typing. 🙂 I can see the justification for it now, still stumped on why it would be necessary. For pennies, sure, but milligrams? ---
**Author:** ![Punoqllads](https://avatars.discourse-cdn.com/v4/letter/p/d2c977/32.png) [@Punoqllads](https://boards.straightdope.com/u/Punoqllads)\ **Post date:** [June 18, 2003, 2:43am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/19 "2003-06-18T02:43:35Z")
It’s not so much that you’re “sure” that the value is 3.5, it’s that your current calculations, including any previous roundings needed, give you the exact number 3.5. Since you don’t know if previous roundings bumped the number up a little or down a little, you pick some fair rule for deciding which way to round. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 18, 2003, 3:45am UTC](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558/20 "2003-06-18T03:45:16Z")
3.5 + 4.5 = 8. Doing the traditional method of rounding up, you’d estimate this to 4 + 6, which is 10. In the banker’s method, you’d estimate it to 4 + 4, which is 8. Can be there any question that the banker’s method is the better? [Next page](https://boards.straightdope.com/t/rules-for-rounding-numbers/182558.md?page=2)