How do you determine the number of zeros to annex in the product of 0.002 and 0.003?

In the first number, 0.002, there are three decimal places. Also, in the second number, 0.003, there are also three decimal places. It is expected therefore that there are 6 digits after the decimal point in the product of the given numbers. Since, the product of 2 and 3 as the latest numbers of the decimal places, the rest of the numbers would be zero. Then, there are five zeros to annex the product of the numbers. A zero should also be placed before the decimal point. 

The product of these numbers is 0.000006.