Malika works as an accountant for a building-materials wholesaler in Andijan. One Friday a sales report reached her desk with a large order: 37 pallets of tiles, each pallet holding 48 boxes, each box priced at 59 dollars. The total in the report was 104,816 dollars.
The client was waiting for the invoice, and Malika had only a minute. She did not multiply the three numbers. Instead she looked only at the last digit of each one. Seven times eight is fifty-six, so the last digit so far was six. Six times nine is fifty-four, so the last digit of the true total had to be four.
The figure in the report ends in six. It could not be right.
She then multiplied properly. Thirty-seven pallets of 48 boxes make 1,776 boxes, and 1,776 boxes at 59 dollars cost 104,784 dollars. The report was 32 dollars too high. A colleague had typed the box count as 1,776 but used an old price for some of the boxes.
Thirty-two dollars is a small error on an order of over a hundred thousand, but the client was a public agency that checks every invoice, and a wrong total would have delayed the payment by weeks.
The last-digit check does not prove that a total is right. It only proves, very quickly, that some totals are wrong. Malika now runs it on every report before anything else.