A gap in the book: swapped digits or a double entry

In the evening you compared your book with the shelf: the book says 54, the shelf holds 45. You recounted, and the shelf really has 45. So nothing is missing; the mistake is in the entry. Quite often a gap comes not from theft but from little slips in the notebook. Finding them takes no complicated arithmetic, only a few simple tricks and a routine.

Five kinds of entry slip

Before hunting for a gap, know what slips usually look like:

1. digits swapped: 54 instead of 45, 72 instead of 27;
2. a line written twice: one sale or receipt entered two times;
3. a line not written: a sale or receipt never reached the book;
4. a wrong sign: an issue instead of a receipt, or the reverse;
5. an extra or missing zero: 100 instead of 10, 20 instead of 200.

All five are commoner when you are rushed, tired or working with long numbers. Once you know them by sight, hunting becomes much quicker.

The divisible-by-nine trick

Step one is to find the gap: subtract the real count from the book figure. If the gap divides by 9 (9, 18, 27, 36, 45 and so on), two neighbouring digits were probably swapped.

Example: the book says 54, the truth is 45, and the gap is 54 − 45 = 9. Another: the book says 72, the truth is 27, the gap is 45, which is 5 × 9. This is no coincidence: when the digits of a two-digit number are swapped, the gap always divides by 9. One warning only: this is not proof but a pointer to where to look. A gap can divide by 9 for other reasons too.

When the gap equals one line

The second trick is to compare the gap with the lines for that item over the last few days.

• If the gap equals the number in a single line exactly, that line was either written twice (the book is higher) or not written at all (the book is lower).
• If the gap is twice the number in a line, a sign may have gone wrong.

For example, the book shows 24 more than the shelf. Yesterday a sale of 12 was entered for this item. 24 = 2 × 12: probably the sale of 12 was entered as a receipt instead of an issue. Halve the gap and you often find the answer right there.

If the gap is very large, for instance several times the shelf count, check for a stray zero first: 10 instead of 100 or the reverse. That slip catches the eye quickly, so it is best checked first.

The search routine

When a gap appears, do not rush. Follow these steps:

1. First recount the shelf and make sure nothing has changed.
2. Write the gap with its sign: "book is 9 higher" or "9 lower".
3. Divide the gap by 9 and by 2 and compare with the lines.
4. Look through the lines since the last good count, for this item only.
5. If you find nothing, write an "adjustment" line and note the reason briefly.

You are searching one item over a few days, not the whole stock, so the job often takes about fifteen minutes.

Once you find the slip, do not merely fix that one line. The balances after it were worked out from the wrong figure, so recalculate them too. Otherwise the corrected slip will show up as a gap again the next day.

Habits that cut slips

• enter large numbers in pairs: one reads, the other writes, then check aloud;
• put a date and a short note on every receipt and issue;
• add up the total at the end of the day, so any slip stays a one-day slip;
• never rub out an old figure: strike it with one line and write the right one beside it.

Each time you find a slip, jot its kind in the margin. After three or four weeks you will see which slip repeats most, and you can adjust your habits; if digits are often swapped, for instance, two people will check large numbers.

Conclusion

A gap in the book is not always a shortage. Knowing the five kinds of slip, the divisible-by-nine pointer, the comparison with a single line and a tidy routine often finds the answer quickly. If a gap cannot be explained this way, a fresh count is needed, and then the Sanab team can run it fast and hand over a list of differences in the report.