Accountants Use 9 to Check for Errors
Date: 02/21/2002 at 23:11:51 From: Steven Etheridge Subject: Number theory I know accountants divide the difference of debits and credits by 9 to check for a transposition error. I need to understand why this works. It may be related to casting out nines, etc., but I can't quite figure it out. Thanks!
Date: 02/22/2002 at 12:31:20 From: Doctor Schwa Subject: Re: Number theory Hi Steven, 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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