Multiplication of Decimal Numbers

🏆Practice multiplication of decimal fractions

We will solve the multiplication of decimal numbers using the vertical multiplication method.
We will proceed in the following order:

  • We will neatly write the multiplication exercise in vertical form – one decimal point under the other decimal point, tenths under tenths, hundredths under hundredths, etc.
  • We will solve the exercise and, for now, will not pay attention to the decimal point.
  • We will strictly adhere to the rules of vertical multiplication.
  • We will review each number in the exercise and find out how many digits there are after the decimal point.
  • We will count the total number of digits after the decimal point (taking into account both numbers) and that will be the number of digits after the decimal point in the final answer.
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Test yourself on multiplication of decimal fractions!

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\( 0.1\times0.999= \)

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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 0.4×0.2=0.4\times 0.2=
We will write it in vertical form making sure that the decimal point is under the other decimal point:

1a - 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 008008
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.

2a - there will be 2 digits after the decimal point in the result

What does this mean?
Let's look at the first number 0.40.4, there is one digit after the decimal point.
Let's look at the second number 0.20.2, there is one digit after the decimal point.

Let's ask: How many digits after the decimal point are there in total? 22
1+1=21+1=2

Therefore, there will be 22 digits after the decimal point in the result.
We will obtain:

3a - Therefore, there will be 2 digits after the decimal point in the result

And this is the final result.


Multiplication Exercises with Decimal Numbers

Exercise 1

0.02×0.09=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:

4a - the decimal point is under the other decimal point

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

5a - Let's add up the number of digits after the decimal point in the numbers of the exercise

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 0.00180.0018 :


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Exercise 2

45.7×0.4=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:

7a - Let's solve it as usual and ignore the decimal point

Let's calculate where to place the decimal point:

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


Exercise 3

15.06×0.01= 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:

9b - Let's write the exercise clearly in vertical form

Let's calculate where to place the decimal point:

Let's apply it in the answer and we will obtain:
That is, 0.15060.1506


Do you know what the answer is?

Exercise 4

13×0.24=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:

11a- Let's write the exercise clearly in vertical form

Let's calculate where to place the decimal point:

Let's apply it in the answer and we will obtain:
03.1203.12  That is, 3.123.12


Examples and exercises with solutions for multiplying decimal numbers

Exercise #1

4.1⋅1.6⋅3.2+4.7=? 4.1\cdot1.6\cdot3.2+4.7=\text{?}

Step-by-Step Solution

We convert decimal numbers into mixed fractions:

4110×1610×3210+4710= 4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=

Now, we convert mixed fractions into simple fractions:

4110×1610×3210+4710= \frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=

We solve the exercise from left to right:

41×1610×10=656100 \frac{41\times16}{10\times10}=\frac{656}{100}

Now we get the exercise:

656100×3210+4710= \frac{656}{100}\times\frac{32}{10}+\frac{47}{10}=

We solve the multiplication exercise:

656×32100×10=20,9921,000 \frac{656\times32}{100\times10}=\frac{20,992}{1,000}

Now we get the exercise:

20,9921,000+4710= \frac{20,992}{1,000}+\frac{47}{10}=

We multiply the fraction on the right so that its denominator is also 1000:

47×10010×100=4,7001,000 \frac{47\times100}{10\times100}=\frac{4,700}{1,000}

We get the exercise:

20,9921,000+4,7001,000=20,992+4,7001,000=25,6921,000 \frac{20,992}{1,000}+\frac{4,700}{1,000}=\frac{20,992+4,700}{1,000}=\frac{25,692}{1,000}

We convert the simple fraction into a decimal number:

25,6921,000=25.692 \frac{25,692}{1,000}=25.692

Answer

25.692

Exercise #2

0.1×0.999= 0.1\times0.999=

Video Solution

Answer

0.0999 0.0999

Exercise #3

0.1×0.35= 0.1\times0.35=

Video Solution

Answer

0.035 0.035

Exercise #4

0.1×0.5= 0.1\times0.5=

Video Solution

Answer

0.05 0.05

Exercise #5

0.1×0.004= 0.1\times0.004=

Video Solution

Answer

0.0004 0.0004

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