Multiplying decimals by decimals: the shortcut
The shortcut for multiplying decimals by decimals is this: you multiply as if there were no decimal points, and then you place a decimal point in the answer in such a manner that the number of decimal digits in the answer is the SUM of the decimal digits in all the factors.
We practice using this rule with several problems, and then I show where the rule comes from, using fraction multiplication.
Consider this example: 2/10 × 6/100 = 12/1000. The number of zeros in the denominator (in the power of ten) corresponds to the number of decimal digits:
2/10 is 0.2 (one decimal digit)
6/100 is 0.06 (two decimal digits)
The answer, 12/1000, is 0.012 (three decimal digits).
As we multiply powers of ten (the denominators), we simply ADD the number of zeros to get the answer. And that is why we ADD the decimal digits to get the amount of decimal digits for the answer
This lesson is meant for 5th grade math (and onward).
Check out also the 1st part of this lesson, where we explore SCALING.
See also
Multiplying decimals and whole numbers: scaling