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.

Suggested Topics to Practice in Advance

  1. Multiplication and Division of Decimal Numbers by 10, 100, etc.
  2. Division of Decimal Numbers

Practice Multiplication of Decimal Fractions

Examples with solutions for Multiplication of Decimal Fractions

Exercise #1

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

0.3×2.15=0645 0.3\times2.15=0645

Video Solution

Step-by-Step Solution

In the number -0.3, there is one digit after the decimal point, 3

In the number 2.15, there are two digits after the decimal point, 15

Therefore, we have three digits after the decimal point.

So, from our result, we will count three decimal places and find that the answer is -0.645

Answer

0.645 0.645

Exercise #2

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

3.5×2.4=840 3.5\times2.4=840

Video Solution

Step-by-Step Solution

In the number -3.5, there is one digit after the decimal point, 5

In the number 2.4, there is one digit after the decimal point, 4

In other words, we have two digits after the decimal point.

Therefore, from our result, we will count three decimal places and find that the answer is 8.40

Answer

8.40 \text{8}.40

Exercise #3

4.11.63.2+4.7=? 4.1\cdot1.6\cdot3.2+4.7=\text{?}

Step-by-Step Solution

We begin by converting the 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}=

We then convert the 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}

This results in the following 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 then 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 obtain 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}

Lastly 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 #4

0.1×0.004= 0.1\times0.004=

Video Solution

Answer

0.0004 0.0004

Exercise #5

0.1×0.999= 0.1\times0.999=

Video Solution

Answer

0.0999 0.0999

Exercise #6

0.1×0.35= 0.1\times0.35=

Video Solution

Answer

0.035 0.035

Exercise #7

0.1×0.5= 0.1\times0.5=

Video Solution

Answer

0.05 0.05

Exercise #8

Find the correct place of the decimal point:

1.35×2.47=33345 1.35\times2.47=33345

Video Solution

Answer

3.3345 3.3345

Exercise #9

0.01×0.50= 0.01\times0.50=

Video Solution

Answer

0.005 0.005

Exercise #10

0.01×0.300= 0.01\times0.300=

Video Solution

Answer

0.003 0.003

Exercise #11

0.01×0.101= 0.01\times0.101=

Video Solution

Answer

0.00101 0.00101

Exercise #12

0.01×0.45= \text{0}.01\times0.45=

Video Solution

Answer

0.0045 0.0045

Exercise #13

0.01×0.315= 0.01\times0.315=

Video Solution

Answer

0.00315 0.00315

Exercise #14

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

3.751×0.5=18755 3.751\times0.5=18755

Video Solution

Answer

1.8755 1.8755

Exercise #15

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

6.13×2.05=125665 6.13\times2.05=125665

Video Solution

Answer

12.5665 12.5665

Topics learned in later sections

  1. Decimal Measurements
  2. Repeating Decimal
  3. Decimal Fractions