If the difference between two columns is divisible by 9, what type of error is it most consistent with?

If the difference between two columns is divisible by 9, what type of error is it most consistent with?

• A. A transposition error where two digits are reversed
• B. An omission of an entry in the general ledger
• C. A slide error where the decimal point was moved
• D. A difference not divisible by 9 indicates no error

Answer: (C)

Divisibility by 9 helps reveal errors that don’t change the digits involved, only their place value. If a decimal point is moved in one entry, the digits themselves remain the same; only how those digits are scaled changes. Since a number’s value modulo 9 is determined by the sum of its digits, moving the decimal does not alter that digit sum. Therefore the entry’s contribution to the column total remains congruent modulo 9 to its original, and the difference between the two column totals ends up being a multiple of 9. For example, if an amount with digits 1, 2, 3, 4, 5 is written as 123.45 or, after sliding the decimal, 12.345, the sum of the digits is still 15 in either form, so their modulo 9 value is the same. This invariance makes a decimal-point slide a plausible cause of a difference that is divisible by 9. Omitting an entry or simply transposing digits doesn’t fit this pattern as cleanly in many practical ledger situations, and a difference not divisible by 9 would typically indicate no error or a different type of error. Hence, a slide of the decimal point is most consistent with a divisible-by-9 discrepancy.

Divisibility by 9 helps reveal errors that don’t change the digits involved, only their place value. If a decimal point is moved in one entry, the digits themselves remain the same; only how those digits are scaled changes. Since a number’s value modulo 9 is determined by the sum of its digits, moving the decimal does not alter that digit sum. Therefore the entry’s contribution to the column total remains congruent modulo 9 to its original, and the difference between the two column totals ends up being a multiple of 9.

For example, if an amount with digits 1, 2, 3, 4, 5 is written as 123.45 or, after sliding the decimal, 12.345, the sum of the digits is still 15 in either form, so their modulo 9 value is the same. This invariance makes a decimal-point slide a plausible cause of a difference that is divisible by 9.

Omitting an entry or simply transposing digits doesn’t fit this pattern as cleanly in many practical ledger situations, and a difference not divisible by 9 would typically indicate no error or a different type of error. Hence, a slide of the decimal point is most consistent with a divisible-by-9 discrepancy.