What is One Way to Check for an Error Caused by Transposed Numbers?

One effective way to check for an error caused by transposed numbers (when two adjacent digits are accidentally swapped, like writing 64 instead of 46) is to use the difference test:

🔍 Check if the difference is divisible by 9

If you subtract the incorrect number from the correct number and the result is divisible by 9, then it’s likely a transposition error.

📌 Example:

Suppose the correct number is 64, but someone wrote 46.

• 64 − 46 = 18

• 18 ÷ 9 = 2, which is divisible by 9 ✅

This suggests a transposition error.

⚠️ Note:

This method works best for adjacent digit transpositions (e.g., swapping digits like 3 and 5 to make 35 into 53), and not for other types of errors like digit omissions or wrong digits.

Here’s how you can check for transposed number errors using a spreadsheet (like Excel or Google Sheets) and also with a quick Python snippet.

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📊 In a Spreadsheet (Excel or Google Sheets)

Assume:

• A1 contains the correct number (e.g., 64)

• B1 contains the potentially incorrect number (e.g., 46)

✅ Formula to check for transposition:

This checks if the absolute difference is divisible by 9.

🐍 In Python

Here’s a small script: