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.

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

Exercise #1

4.11.63.2+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

0.1×0.5= 0.1\times0.5=

Video Solution

Answer

0.05 0.05

Exercise #3

0.1×0.35= 0.1\times0.35=

Video Solution

Answer

0.035 0.035

Exercise #4

0.1×0.999= 0.1\times0.999=

Video Solution

Answer

0.0999 0.0999

Exercise #5

0.1×0.004= 0.1\times0.004=

Video Solution

Answer

0.0004 0.0004

Exercise #1

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 #2

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

0.3×2.15=0645 0.3\times2.15=0645

Video Solution

Answer

0.645 0.645

Exercise #3

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

2.5×0.13=0325 2.5\times0.13=0325

Video Solution

Answer

0.325 \text{0}.325

Exercise #4

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

Exercise #5

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

3.5×2.4=840 3.5\times2.4=840

Video Solution

Answer

8.40 \text{8}.40

Exercise #1

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 #2

0.01×0.45= \text{0}.01\times0.45=

Video Solution

Answer

0.0045 0.0045

Exercise #3

0.01×0.315= 0.01\times0.315=

Video Solution

Answer

0.00315 0.00315

Exercise #4

0.01×0.101= 0.01\times0.101=

Video Solution

Answer

0.00101 0.00101

Exercise #5

0.01×0.300= 0.01\times0.300=

Video Solution

Answer

0.003 0.003

Topics learned in later sections

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