Editing ABA routing transit number (section)

====Check digit====
The ninth, [[check digit]] provides a [[checksum]] test using a position-weighted sum of each of the digits. High-speed check-sorting equipment will typically verify the checksum and if it fails, route the item to a reject pocket for manual examination, repair, and re-sorting. Mis-routings to an incorrect bank are thus greatly reduced.

The following condition must hold:<ref name="bo04" />

:{{math|1=(3({{var|d}}{{sub|1}} + {{var|d}}{{sub|4}} + {{var|d}}{{sub|7}}) + 7({{var|d}}{{sub|2}} + {{var|d}}{{sub|5}} + {{var|d}}{{sub|8}}) + ({{var|d}}{{sub|3}} + {{var|d}}{{sub|6}} + {{var|d}}{{sub|9}})) mod 10 = 0}}

: ([[Modulo operation|Mod]] or modulo is the remainder of a division operation.)
In terms of weights, this is 371 371 371. This allows one to catch any single-digit error (incorrectly inputting one digit), together with most transposition errors. 1, 3, and 7 are used because they (together with 9) are [[coprime]] to 10; using a coefficient that is divisible by 2 or 5 would lose information (because <math>5 \cdot 0 = 5 \cdot 2 = 5 \cdot 4 = 5 \cdot 6 = 5 \cdot 8 = 0 \mod 10</math>), and thus would not catch some substitution errors. These do not catch transpositions of two digits that differ by 5 (0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9), but captures other transposition errors.{{citation needed|date=April 2013}}

As an example, consider 111000025 (which is a valid routing number of [[Bank of America]] in [[Virginia]]). Applying the formula, we get:

: {{math|1= (3(1&thinsp;+&thinsp;0&thinsp;+&thinsp;0) + 7(1&thinsp;+&thinsp;0&thinsp;+&thinsp;2) + (1&thinsp;+&thinsp;0&thinsp;+&thinsp;5)) mod 10 = 0}}.