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Multiplying Decimals

Learn multiplying decimals concept. In mathematics, the decimal values are most important one. The decimal values will display an accurate value. Commonly, the decimal values will form from the fraction number. Here, we are going to discuss the topic of decimal multiplication and their rules with some example problems. We need to multiply the decimal values. The decimal value of the fraction $\frac{2}{4}$ is 0.5.

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How to Multiply Decimals

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Many rules for multiplying decimals values; some of them are following below :

Step 1: we need to convert the decimal value into real value then we can easily multiply the value.

Step 2: Now, we need to check how many digits are present after the point.

Step 3: If only one digit is present after the value then we need to multiply with the value 10 for removing the point.

For example, 0.5

Here 0.5 is the decimal value we are going to multiply with the value 10

$\frac{0.5\times10}{10}$ = $\frac{5}{10}$

If there are two digits present after the point we need to multiply with the value 100 for removing the point.

$\frac{0.55\times100}{100}$ = $\frac{55}{100}$

If there are three digits present after the point we need to multiply with the value 1000 for removing the point.

$\frac{0.555\times1000}{1000}$ = $\frac{555}{1000}$

Multiplying with Decimals

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Below are examples on multiplying with decimals :

Solved Examples

Question 1: Multiply the decimal values 12.5 × 5.5
Solution:
First, we need to convert the given decimal number into real number
The value 12.5 has only one present after the point, so we need to multiply 10 with the given number
$\frac{12.5\times10}{10}$ = $\frac{125}{10}$
Then the next number 5.5, this number also has only one digit after the point, so
$\frac{5.5\times10}{10}$ = $\frac{55}{10}$

Now, we are going to multiply the numbers
1 2 5 
× 5 5
---------------
6 2 5
6 2 5 +
-----------------
6 8 7 5
-----------------
Now, divide the answer by 100
$\frac{6875}{100}$


Correct answer is 68.75
Question 2: Multiply the decimal values 95. 210 × 4.28
Solution:

First, we need to convert the given decimal number into real number

The value 95.210 has three digits after the point actually, there are three digits present but we need not consider the value zero, so we are going to multiply 100 with the given number

$\frac{95.210\times100}{100}$ = $\frac{9521}{100}$

Then the next number 4.28, this number has two digits after the point, so

$\frac{4.28\times100}{100}$ = $\frac{428}{100}$

Now, we are going to multiply the numbers

9 5 2 1

× 4 2 8

-------------------------
7 6 1 6 8

1 9 0 4 2 +

3 8 0 8 4 + +

----------------------------

4 0 7 4 9 8 8

-----------------------------
Now divide the answer by 10000

$\frac{4074988}{10000}$



Correct answer is 407.4988

Practice Problems

Question 1: Multiply the decimal values 5.645 × 9.7
Question 2: Multiply the decimal values 10.000 × 10.00

Multiplying Decimals by Whole Numbers

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Decimal number is a number with the base 10. The preparation for multiplying decimals is similar as the way of multiplying the given number considering it as a whole numbers. However, for multiplying decimals we must be careful to correctly place the decimal point after the product for multiplication. In the preparation for multiplying decimals, the number of decimal places in the answer must equal the total number of places to the right of the decimal point in the problem.

Solved Example

Question: Multiply 11.8 x 4
Solution:
Write this as 118
                          x 4
                        -------------
                            472
                       --------------
There is one figure after the decimal point in the question, so there must be only one after the point in the answer.

11.8 x 4 = 47.2


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