# Multiplying Decimals – Definition with Examples

## Introduction of Multiplying Decimals

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## Multiplying Decimals with Whole Number

Multiplying a decimal number with a whole number is similar to multiplying whole numbers. However, the decimal places in one of the numbers can make it seem difficult. So, let us see how we can simplify the process for you.

Step 1: Forget about the decimals. Yes, they don’t play any role while you are performing the actual operation. Now, multiply the two numbers as you would do with whole numbers.

Step 2: Count the number of digits after the decimal point.

Step 3: Place the decimal point in the product leaving the same number of digits from the right as the decimal places in the factor.

Pro Tip: Always remember that the product after multiplication must have the same number of decimal places as the factors.

Now, let us look at examples of multiplying decimals:

Example: Find the product of $0.2 \times 3$

Step 1: We take the two numbers without considering the decimal, i.e., 2 and 3. We multiply them. So, we get $2 \times 3 = 6$.

Step 2: We count the number of digits after the decimal point. Here we have just one digit after the decimal.

Step 3: We place the decimal point in the product leaving behind one digit from the right. Since the product is 6, we have to place the decimal before it.

So, the answer will be 0.6.

Example: Find the product of $0.4 \times 3$

Similarly to find the product of 0.4 and 3, multiply the numbers without decimals i.e $4 \times 3 = 12$.

Now there’s one digit after decimal point so let’s place the decimal point in the product leaving behind one digit from the right : 1.2

So $0.4 \times 3 = 1.2$

## Multiplication of Two Decimal Numbers

While multiplying two decimal numbers, you must consider the decimal places of both factors.

Step 1: Ignore the decimal places initially. Perform the multiplication of the given numbers.

Step 2: Counter the number of decimal places in both the factors and calculate the sum of the same.

Step 3: Place the decimal point from the right end according to the number of decimal places you calculated in step 2.

Example: Find the product of $15.62 \times 0.7$

Step 1: We ignore the decimals and multiply the given numbers.

$1562 \times 7 = 10934$

Step 2: We count the number of decimal places in both the numbers and calculate their sum.

15.62 has 2 decimal places, and 0.72 has 1 decimal place. Therefore, the sum of the decimal factors is 3.

Step 3: We place the decimal in the product leaving behind three digits from the right.

So, $15.62 \times 0.7 = 10.934$

## Multiplication of Decimals by 10, 100, and 1000

When we multiply a decimal number by 10, the decimal shifts to the right of the number by one place.

For example, $15.2705 \times 10 = 152.705$

Here, only one change takes place in the solution: the decimal shift from its position in 15.2705 to one place to the right. So, we get 152.705 as the answer.

When we multiply a decimal number by 100, the decimal shifts to the right of the number by two places.

For example, $15.2705 \times 100 = 1527.05$

When we multiply a decimal number by 1000, the decimal shifts to the right of the number by three places.

For example, $15.2705 \times 1000 = 15270.5$

So, when we have to multiply a decimal number by 10, 100, or 1000, we shift the decimal to the right of the number according to the number of zeros behind 1.

Let us consider a few examples:

• $53.5 \times 10 = 535$
• $469.127 \times 10 = 4691.27$
• $398.16 \times 100 = 39816$
• $826.3 \times 100 = 82630.0$
• $0.137 \times 100 = 13.7$

## Solved Examples

1) Find the product of $9.2 \times 0.08$.

Solution:

Step 1: We ignore the decimals and multiply the given numbers.

$92 \times 8 = 736$

Step 2: We observe that 9.2 has 1 decimal place, and 0.08 has 2 decimal places. Therefore, the sum of the decimal factors is 3.

Step 3: We place the decimal in the product leaving behind three digits from the right.

So, $9.2 \times 0.08 = 0.736$

2) Find the product of $20.1 \times 6.0$.

Solution:

Step 1: We ignore the decimals and multiply the given numbers.

$201 \times 60 = 12060$

Step 2: We observe that 20.1 has 1 decimal place, and 6.0 has 1 decimal place. Therefore, the sum of the decimal factors is 2.

Step 3: We place the decimal in the product leaving two digits from the right.

So, $20.1 \times 6.0 = 120.60$

3) Find the product of $36 \times 0.5$.

Solution:

Step 1: We ignore the decimal and multiply the given numbers.

$36 \times 5 = 180$

Step 2: We observe that 0.5 has 1 decimal place.

Step 3: We place the decimal in the product leaving behind one digit from the right.

So, $36 \times 0.5= 18.0$

## Practice Problems

1

### What will you get if you multiply 341.58 with 4?

136632
1366.32
136.623
13363.2
CorrectIncorrect
We ignore the decimal and multiply the given numbers.
We get $34158 \times 4 = 136632$
Since $341.58$ has two decimal places, we place the decimal in the product leaving two digits from the right.
So, the answer is $1366.32$.
2

### Which one of the following is the right answer for the given multiplication problem? $64 \times 8.3$

531.2
351.2
53.12
5.312
CorrectIncorrect
We ignore the decimal and multiply the given numbers.
We get $64 \times 83 = 5312$
Since $8.3$ has one decimal place, we place the decimal in the product leaving behind one digit from the right.
So, the answer is $531.2$
3

### Find the product of $5.27 \times 3.9$.

2055.3
17.553
20.553
25.053
CorrectIncorrect
We ignore the decimals and multiply the given numbers.
We get $527 \times 39 = 20553$
Since 5.27 has two decimal places and 3.9 has one decimal place, we place the decimal in the product leaving behind three digits from the right.
So, the answer is $20.553$.

For example, $4.89 \times 10= 48.9$ and $3.4 \times 100 = 340$