During decimal multiplication, we know that the placement of the decimal point in the product is decided by the sum of number of digits after the decimal point in both the factors being multiplied.

Question

I know that's what we do but i don't understand why this rule works?What's the reasoning behind it?

Answer 1

In google type :

Multiplying and dividing decimals, multiply two or more decimals.

When you see list of results click on :

w w w . m o n t e r e y i n s t i t u t e . o r g

Answer 2

34.56
x3.002

is the same as 34x3 + 34x.002 + .56x3+.56x.002

so now note. the final decimal place will be decided by the last term above, .56x.002, or .00112 (five digits), which is the sum of the digits of the two numbers being multiplied.