Why should decimal points be added to align with decimal points but not when multiplied

This paper focuses on the problem that "decimal points need to be aligned to the decimal point when adding decimal numbers, and decimal numbers need not be aligned". It compares the rule of adding integers to align the number of digits, explains that the logic of decimal addition is "aligned to the left", and mentions the ancient people's naming of decimal places. It explains the reason why multiplication does not need to be aligned, and gives specific examples to prove it.

Why should decimal points be added to align with decimal points but not when multiplied

When adding integers, they must be aligned. Integers have differences in different digits such as one, ten, hundreds, thousands, and tens of thousands. You cannot add the number in one place to the number in ten digits, or the number in thousands to the number in ten thousand digits. When adding integers, the need to "align" is a kind of "align to the right." The addition of decimal numbers is a kind of "alignment to the left."

The ancients in China have long noticed this, and they have given names to everyone after the decimal point, such as minute, millimeter, millimeter, silk, and sudden. For the case where both integers and decimals are combined, then the "decimal point" must be used as the "watershed" to perform addition and subtraction operations.

However, when multiplying decimal numbers, the decimal points do not need to be aligned. In fact, decimal numbers are just fractions with 10, 100, 1000... as denominator. Fractions with different denominators can still be multiplied, which is clear by looking at the following example.

0.1×0.27×0.004=0.000108.