8.1. Petya made a mistake when writing a decimal fraction: he wrote the digits correctly, but moved the decimal point one position. As a result, he got a number that was 19.71 less than the required one. What number should Petya have written?
Answer: 21.9.

Solution. Since the number decreased as a result of the error, the decimal point must have been moved to the left. In doing so, the number was reduced by a factor of 10. Let the resulting number be \(x\), then the required number is 10x. According to the problem: \(10x - x = 19.71\), hence, \(x = 2.19, 10x = 21.9\).

Grading Criteria.

“+” A complete and justified solution is provided

“±” A correct reasoning is provided, but a computational error is made

“±” The correct equation and answer are provided, but it is not explained why the decimal point moved to the left

“干” Only the correct answer is provided

“-” The problem is not solved or is solved incorrectly