# What is this mathematical procedure called? **URL:** \ **Category:** Factual Questions\ **Created:** [October 9, 2007, 1:43am UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020 "2007-10-09T01:43:40Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [October 9, 2007, 1:43am UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/1 "2007-10-09T01:43:40Z")
Take a multi-digit number. Add up all of the digits. Add up the digits in the sum. Keep adding like this until you arrive at a single digit. Is there a name for these numbers? To give an example: 655,587,010,432 6+5+5+5+8+7+1+4+3+2=46 4+6=10 1+0=1 ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [October 9, 2007, 1:49am UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/2 "2007-10-09T01:49:11Z")
The [digital root](http://en.wikipedia.org/wiki/Digital_root). ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [October 9, 2007, 3:00am UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/3 "2007-10-09T03:00:01Z")
The procedure is usually called “casting out nines.” A slightly faster method is to add the digits (which gives 46 in your example) and then take the remainder when that’s divided by 9. So 1 is the result. ---
**Author:** ![F.U.Shakespeare](https://avatars.discourse-cdn.com/v4/letter/f/aca169/32.png) [@F.U.Shakespeare](https://boards.straightdope.com/u/F.U.Shakespeare)\ **Post date:** [October 9, 2007, 3:14am UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/4 "2007-10-09T03:14:30Z")
What Wendell said. Where I grew up, ‘casting out the nines’ was commonly taught as a way to check for errors in arithmetic (which admittedly wouldn’t catch errors of misplacing digits [e.g., writing 123 as 132). ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [October 9, 2007, 9:16pm UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/5 "2007-10-09T21:16:14Z")
“Casting out nines” is even faster if you actually do that, i.e., drop all 9s and any combination of digits that add to 9. In the OP’s example: 655,587,010,432 655587010432 5558701042 55870102 558010 5500 5+5 = 10 1+0 = 1 ---
**Author:** ![Projammer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/projammer/32/559_2.png) [@Projammer](https://boards.straightdope.com/u/Projammer)\ **Post date:** [October 9, 2007, 9:26pm UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/6 "2007-10-09T21:26:05Z")
[QUOTE=F. U. Shakespeare] What Wendell said. Where I grew up, ‘casting out the nines’ was commonly taught as a way to check for errors in arithmetic (which admittedly wouldn’t catch errors of misplacing digits [e.g., writing 123 as 132). [/QUOTE] Okay. I’ll bite. How does this technique check for errors? I’m asking here instead of google because I’m pretty sure I’m not the only one wondering. ---
**Author:** ![Terminus\_Est](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/terminus_est/32/3087_2.png) [@Terminus\_Est](https://boards.straightdope.com/u/Terminus_Est)\ **Post date:** [October 9, 2007, 9:34pm UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/7 "2007-10-09T21:34:12Z")
[QUOTE=Projammer] Okay. I’ll bite. How does this technique check for errors? I’m asking here instead of google because I’m pretty sure I’m not the only one wondering. [/QUOTE] From the Wikipedia article cited by **Q.E.D.** : > [@](#): > > Digital roots can be used as a sort of checksum. For example, since the digital root of a sum is always equal to the digital root of the sum of the summands’ digital roots, somebody adding long columns of large numbers will often find it reassuring to apply casting out nines to his or her result — knowing that this technique will catch the majority of errors. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 9, 2007, 10:17pm UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/8 "2007-10-09T22:17:45Z")
[QUOTE=Terminus Est] From the Wikipedia article cited by **Q.E.D.** : > [@](#): > > Digital roots can be used as a sort of checksum. For example, since the digital root of a sum is always equal to the digital root of the sum of the summands’ digital roots, somebody adding long columns of large numbers will often find it reassuring to apply casting out nines to his or her result — knowing that this technique will catch the majority of errors. [/QUOTE] For those of you following at home, this is saying that casting out nines can prove the presence of certain errors. It doesn’t say that casting out nines can prove the absence of all errors, because it can’t. Transpose two digits and casting out nines gives the same result. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [October 9, 2007, 10:21pm UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/9 "2007-10-09T22:21:58Z")
Am I the only one here seeing some guy going through the math classes with a wheelbarrow, crying out “Cast out your nines, cast out your nines!!” 😃 ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [October 9, 2007, 11:01pm UTC](https://boards.straightdope.com/t/what-is-this-mathematical-procedure-called/422020/10 "2007-10-09T23:01:58Z")
Could this be an example of a parrotty error? 😃 😃