Multiplication of Decimal Numbers

To easily solve exercises involving the multiplication of decimal numbers, you should know how to solve multiplications of whole numbers using the vertical form.
The most recommended method for solving exercises of this type is, clearly, multiplication in vertical form.
Steps to follow:

• • We will write the exercise clearly in vertical form – decimal point under the other decimal point, tenths under tenths, hundredths under hundredths, and so on.
• • We will solve the exercise without taking the decimal point into account, but remembering that it exists.
• • Let's not stop acting according to the rules of multiplication in vertical form, that is, reserving places for zeros, carrying over remainders and remembering them, etc.
• • We will count the total number of digits after the decimal point (taking into account both numbers) and in this way determine the number of digits that will be after the decimal point in the result.

Let's apply the solution steps in an exercise, this will help you understand it better:
Given the exercise $0.4\times 0.2=$
We will write it in vertical form making sure that the decimal point is under the other decimal point:

Let's solve the exercise as we always do, remembering the rules of multiplication in vertical form.

Notice: for now we ignore the decimal point and do not note it in the result.
We obtained the result $008$
How will we know where to place the decimal point in the result?
Let's look at the numbers in the exercise and add up the number of digits after the decimal point in both numbers.

What does this mean?
Let's look at the first number $0.4$, there is one digit after the decimal point.
Let's look at the second number $0.2$, there is one digit after the decimal point.

Let's ask: How many digits after the decimal point are there in total? $2$
$1+1=2$

Therefore, there will be $2$ digits after the decimal point in the result.
We will obtain:

And this is the final result.

$0.02\times 0.09=$

Solution:
We will write the exercise in vertical form making sure that the decimal point is under the other decimal point:

We will solve it as usual, ignoring the decimal point:

Let's add up the number of digits after the decimal point in the numbers of the exercise and apply the result in the final answer:

Let's apply this to the result and we will get $0.0018$ :

$45.7\times 0.4=$

Solution:
Let's write the exercise clearly in vertical form.
Let's solve it as usual and ignore the decimal point.
We will obtain:

Let's calculate where to place the decimal point:

Let's apply it to the answer and we will obtain: $18.28$

$15.06\times 0.01=$

Solutionן:
Let's write the exercise clearly in vertical form.
Let's solve it as usual and ignore the decimal point in the result.
We will obtain:

Let's calculate where to place the decimal point:

Let's apply it in the answer and we will obtain:
That is, $0.1506$

$13\times 0.24=$

Solution:
Let's write the exercise clearly in vertical form.
Let's solve it as usual and ignore the decimal point in the result.

We will obtain:

Let's calculate where to place the decimal point:

Let's apply it in the answer and we will obtain:
$03.12$ That is, $3.12$