How to determine places of precision needed when taking product of two numbers?

Question

If I have two numbers 0.01 and 0.002 (one with two decimals of precision and the other with three decimals), how can I determine how many decimals of precision are needed for the potential result of 0.00002?

Answer 1

As it turns out there is a rule regarding this:

Multiplication of a Decimal Number by another Decimal Number

The rule states that you can simply count the number of decimals in two numbers and their product will have the precision of the sum of the decimals of those two numbers.

For instance:

 0.02    (two decimals)
x0.003   (three decimals)
========
 0.00006 (five decimals)

Answer 2

In usual usage, $0.01$ and $0.002$ each have one digit of precision. The leading zeros just position the decimal point. Their product should also be quoted with one digit of precision, which is $0.00002$, because the rule is you quote the lower number of digits in your result.