Transposition
The material on Divisibility on our frequently asked questions page,
http://mathforum.org/dr.math/faq/
may well answer your question. It talks about how you can tell whether
a number is divisible by 9.
The idea is that if you have digits a,b in some number, with place
value the "a" is "worth" a * 10^n and b is worth b * 10^(n-1). So in
total the ab is worth a * 10^n + b * 10^(n-1), or 10^(n-1) * (10a + b)
When you switch them, the "ba" is then worth 10^(n-1) * (10b+a).
So the difference is 10^(n-1) * (9a - 9b), which is sure to be
divisible by 9.
The most common other type of error is a single-digit change, which
will only be divisible by 9 if you switch a 9 with a 0, so most of the
time, if your error is divisible by 9, it's due to a transposition.
- Doctor Schwa, The Math Forum
http://mathforum.org/dr.math/
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