 # Multiplication of Decimals – Definition, Facts, Examples | How to Multiply Decimals by Whole Numbers & Powers of 10?

Multiplication is an important arithmetic operation in maths for primary level students. The concept of multiplication will be a more interesting concept than addition for the students. Multiplying decimals is similar to multiplying whole numbers except for the placement of the decimal point in the result. Read this article thoroughly to know what is meant by multiplication of decimals, how to multiply with decimal numbers with a brief explanation.

## Multiplication of Decimals – Definition

Decimal numbers are the standard system for denoting integer and non-integer numbers. The multiplication of decimals is the same as the multiplication with whole numbers. In this concept, the decimals are multiplied by neglecting the points. After multiplication, add the decimal points to the result. Here we provide some examples on multiplication with decimal numbers for better understanding.

### How to Multiply Decimals?

Multiplication of decimals has few simple rules to follow.
1. First count the total number of decimal places contained in both multiplicand and multiplier.
2. Ignore the decimals and right-align the numbers one on top and the other at the bottom.
3. Multiply the numbers.
4. Now insert a decimal point in the product so it has the same number of decimal places equal to the total.
Let us consider an example so that you can know what is the multiplication of decimal numbers.
Example: Multiply two decimal numbers 0.24 and 0.3
Solution:
There are 3 decimal points in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.

Rewrite the product with 3 total decimal places.
Therefore, the multiplication of two decimal numbers 0.24 and 0.3 is 0.072.

### Multiplication of Decimals with Whole Numbers

In this case, we multiply the decimal number with another non-decimal number i.e, whole number. First, multiply the two numbers by neglecting the points. After that count, the decimal points and place the points in the result from the left side.
Example: Multiply two numbers 1.5 and 3
Solution:
There is only a decimal point in the given number.
Ignore the decimal places and complete the multiplication as if operating on two integers. Now add the decimal point in the result.
So, the product of the decimals 1.5 and 3 becomes 4.5

### Multiplying a Decimal by Powers of 10

Multiplying a decimal by powers of 10 means shifting the decimal point to the right as many places as the number of zeros in the power of 10.
Example: Multiply 1.5 and 10
Solution:
Here we see one zero. So shift 1 point to the right.
So it becomes 1.5 × 10 = 15

### Examples of Multiplying Decimals

Example 1.
Multiply 4.52 and 2.1
Solution:
Given the numbers 4.52 and 2.1
There is a total of 4 decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers. Rewrite the product with decimal places. Shift 4 decimal points from left to right.
Thus multiplication of two decimal numbers 0.24 and 0.24 is 0.0576

Example 2.
Multiply the decimals 10.24 and 0.2
Solution:
Given the numbers 10.24 and 0.2
There is total of 3 decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers. Rewrite the product with 3 total decimal places. Shift 3 decimal points from left to right.
Thus multiplication of two decimal numbers 10.24 and 0.2 is 2.048

Example 3.
Multiply the decimals 0.24 and 0.24
Solution:
Given the numbers 0.24 and 0.24
There is total 4 decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers. Rewrite the product with 4 total decimal places from left to right.
Thus multiplication of two decimal numbers 0.24 and 0.24 is 0.0576

Example 4.
Multiply the decimals 2.56 and 3.2
Solution:
Given the numbers 2.56 and 3.2
There is total 3 decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers. Rewrite the product with 3 total decimal places.
Thus multiplication of two decimal numbers 2.56 and 3.2 is 8.192

Example 5.
Multiply the decimals 3.14 and 2.27
Solution:
Given the numbers 3.14 and 2.27
There is total 4 decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers. Rewrite the product with 4 total decimal places from left to right.
Thus multiplication of two decimal numbers 3.14 and 2.27 is 7.1278

### FAQs on Multiplication of Decimals

1. What happens when you multiply decimals?

When you multiply decimals, the decimal point is placed in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.

2. What are the steps in multiplying decimals?

Step 1: Ignore the decimal point and multiply both the numbers.
Step 2: Count the number of decimal places in the decimal number.
Step 3: Then, place the decimal point in the product such that the number of decimal places in the product and the original decimal number should be the same.

3. Why is it important to know how do you solve problems involving decimals?

It is helpful to relate the decimal numbers to something you can understand easier, such as money.

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