Class 7 - Multiplication of Decimals

Multiplication of decimals is an essential skill in maths that is used in everyday situations like handling money, measuring distances, or calculating totals. Learning simple rules like ignoring decimal points during multiplication and placing them correctly in the final answer helps master this topic with ease. In this guide, you’ll learn simple methods to multiply decimals, along with clear examples to master the addition and subtraction of decimals.

Table of Contents

• How to Multiply Decimals
• Multiplication of Decimals by 10, 100, and 1000
• Multiplication of a Decimal by a Whole Number
• Multiplication of a Decimal Number by a Decimal Number
• Solved Examples of Multiplication of Decimals

How to Multiply Decimals

Multiplication of decimals is the process of multiplying numbers that include decimal points. 

Here are the most important rules you must remember to multiply decimals:

1.  Ignore the decimal point first: Multiply the numbers as if they were whole numbers.

2. Count total decimal places: Count digits after the decimal in both numbers.

3.  Place the decimal in the answer: The product must have the same total number of decimal places. 

 

Multiplication of Decimals by 10, 100, and 1000

To multiply a decimal number by 10, 100, and 1000, move the decimal point in the multiplicand to the right by the number of places equal to the number of zeros in the multiplier.

 

 

For example, 

• 2.35 × 10 = 23.5

• 4.7 × 100 = 470
  
  

Multiplication of Decimal by Whole Number

To multiply a decimal by a whole number:

• Multiply the decimal without the decimal point by the whole number.

• Mark the decimal point in the product from right to left so that the number of decimal places in the product is same as the number of decimal places in the decimal number.

 

For example: Multiply: 12 × 0.25
12 × 25 = 300
Number of decimal places = 2
Therefore, 12 × 0.25 = 3.00 = 3

Multiplication of Decimal Number by Decimal Number

To multiply a decimal number with a decimal number, multiply the decimal numbers without a decimal point.

Count the number of decimal places in both the factors.

Mark the decimal point in the product from right to left so that the number of decimal places in the product is the sum of the decimal places in the factors.

For example: Multiply: 2.34 × 1.2
234 × 12 = 2808
Number of decimal places = 2 + 1 = 3
Therefore, 2.34 × 1.2 = 2.808.

Solved Examples of Multiplication of Decimals

Example 1: Multiply: 8.235 × 2.3
Solution: 8235 × 23 = 189405
Number of decimal places = 3 + 1 = 4
Therefore, 8.235 × 2.3 = 18.9405.

Example 2: If Kapil can run 10.96 km in one hour, how far can he run in 5.6 hours?
Solution: Distance covered in 1 hour = 10.96 km
Distance covered in 5.6 hours = 10.96 × 5.6 km

   1096×  56     6576+ 54800   61376

Number of decimal places = 1 + 1 = 2
10.96 × 5.6  = 61.376
Therefore, Distance covered in 5.6 hours = 61.376 km

Example 3: A rectangular park has dimensions 36.85 m × 23.5 m. What is the perimeter of the park?
Solution: Perimeter = 2 × (length + breadth)
Given: Length = 36.85 m; Breadth = 23.5 m
l + b = 36.85 + 23.5 = 60.35
2(l + b) = 2 × 60.35 = 120.70
Therefore, the perimeter of the park is 120.7 m.

Example 4: A sugarcane plant grows about 11.43 cm each day. Find the growth in one week.
Solution: Given that the sugarcane plant grows about 11.43 cm each day.
Growth in one week = 11.43 × 7 = 80.01
Therefore, the growth of the sugarcane plant in one week is 80.01 cm