# Is there an **official** name for the following "digit reduction" operation? [closed]

In one of my programs I have a function I call reduce(n) which associates to n the recursive sum of n's digits until this sum is one digit long. For example:

• 12 -> [1, 2] => 3
• 149 -> [1, 4, 9} -> 14 -> [1, 4] => 5
• and so on

Is there an official name for this operation ?

• Digital root: en.wikipedia.org/wiki/Digital_root Aug 1 at 16:08
• Also called "casting out nines" en.wikipedia.org/wiki/Casting_out_nines Aug 2 at 12:39
• As @GeraldEdgar comments: definitely "casting out nines"... is the name this procedure (and extensions) has and has had for more than 100 years in the U.S. My grandparents (fairly literate, born c. 1890) knew this procedure (as a way to check accuracy of arithmetic... since this process gives a ring homomorphism of the integers to the integers mod 9). Aug 4 at 21:18