Multiplication of decimal fractions - Examples, Exercises and Solutions

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.

Practice Multiplication of decimal fractions

Exercise #1

$4.1\cdot1.6\cdot3.2+4.7=\text{?}$

Step-by-Step Solution

We convert decimal numbers into mixed fractions:

$4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

Now, we convert mixed fractions into simple fractions:

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=$

We solve the exercise from left to right:

$\frac{41\times16}{10\times10}=\frac{656}{100}$

Now we get the exercise:

$\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}=$

We solve the multiplication exercise:

$\frac{656\times32}{100\times10}=\frac{20,992}{1,000}$

Now we get the exercise:

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

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

$\frac{47\times100}{10\times100}=\frac{4,700}{1,000}$

We get the exercise:

$\frac{20,992}{1,000}+\frac{4,700}{1,000}=\frac{20,992+4,700}{1,000}=\frac{25,692}{1,000}$

We convert the simple fraction into a decimal number:

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

25.692

Exercise #2

$0.1\times0.5=$

Video Solution

$0.05$

Exercise #3

$0.1\times0.35=$

Video Solution

$0.035$

Exercise #4

$0.1\times0.999=$

Video Solution

$0.0999$

Exercise #5

$0.1\times0.004=$

Video Solution

$0.0004$

Exercise #1

Find the correct place of the decimal point:

$1.35\times2.47=33345$

Video Solution

$3.3345$

Exercise #2

Given the following exercise, find the correct place of the decimal point:

$0.3\times2.15=0645$

Video Solution

$0.645$

Exercise #3

Given the following exercise, find the correct place of the decimal point:

$2.5\times0.13=0325$

Video Solution

$\text{0}.325$

Exercise #4

Given the following exercise, find the correct place of the decimal point:

$6.13\times2.05=125665$

Video Solution

$12.5665$

Exercise #5

Given the following exercise, find the correct place of the decimal point:

$3.5\times2.4=840$

Video Solution

$\text{8}.40$

Exercise #1

Given the following exercise, find the correct place of the decimal point:

$3.751\times0.5=18755$

Video Solution

$1.8755$

Exercise #2

$\text{0}.01\times0.45=$

Video Solution

$0.0045$

Exercise #3

$0.01\times0.315=$

Video Solution

$0.00315$

Exercise #4

$0.01\times0.101=$

Video Solution

$0.00101$

Exercise #5

$0.01\times0.300=$

Video Solution

$0.003$