Decimal numbers are constituted of two parts. The part before the decimal point is known as the whole number part and the part after the decimal point is known as the fractional part. For example, consider the decimal numbers 59.650 and 64.340. In these decimal numbers, 59 and 64 are the whole numbers, whereas 0.650 and 0.340 are fractional parts of these decimal numbers.

How to Multiply Decimal Numbers

We know that to add or subtract the decimal numbers, we line them up in such a way that units are under units, tens are under tens, hundreds are under hundreds, tenths are under tenths, hundredths are under hundredths and so on. The multiplication of the decimal numbers is slightly different from addition or subtraction. The process of multiplying two decimal numbers is given below:

  1. Multiply the decimal numbers as if they are whole numbers. It simply means that eliminate the decimal point and do not consider it for a while.
  2. Line up the numbers in the same way as we line up the digits while performing addition or subtraction.
  3. Start multiplication from the right, Multiply each digit in the upper number by each digit in the bottom number. This process is exactly like you are multiplying the whole numbers together.
  4. Sum up the products obtained after multiplication.
  5. Count the number of decimal places in both the numbers and add them together. Starting from the right direction, move the decimal point to the left equal to the total number of decimal places in both the numbers.

The product is a decimal number that has a number of decimal places equal to the sum of the number of decimal places of the two factors. The multiplication of the decimal numbers will be further explained through the following examples in this article.

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Example 1

Solve 46.562 · 38.6.

Solution

\begin{array}{ccccccccccc} & &46.562 && \\ \times & & 38.6& & & & \\ \cline{3-5} & &279372& & \\ & &372496~~~& & \\ & &139686~~~~~~~& & \\ \cline{3-5} & &1797.2932~~~~~& & \\ \end{array}

You can see that the numbers 46.562 and 38.6 have 4 decimal places altogether. Therefore, after multiplying the numbers like integers and adding the products, we moved the decimal point 4 places to the left.

 

Example 2

Solve 18.271 · 10.3.

Solution

We will multiply the above two numbers like integers.

\begin{array}{ccccccccccc} & &18.271 && \\ \times & & 10.3& & & & \\ \cline{3-5} & &54813& & \\ & &00000~~~& & \\ & &18271~~~~~~~& & \\ \cline{3-5} & &188.1913~~~~~~& & \\ \end{array}

 

The numbers 18.271 and 10.3 have 4 decimal places altogether. After multiplying 18271 and 103 as integers or whole numbers, we moved the decimal point four places to the left in the resulting answer.

 

Example 3

A car is traveling with a speed of 65 kilometers per hour. How much distance the car will travel in 5 hours 35 minutes?

Solution

First of all, we should know that the distance is equal to the product of speed and time. The time is 5 hours 35 minutes. We can write this time in a decimal form because two different units are used. 5 hours 35 minutes is equal to 5.35 hours. The next step is to multiply 5.35 with a speed of 65 kilometers per hour.

As we can see that one factor in the above question is in decimal form. Therefore, we will eliminate the decimal point and multiply 65 and 535 as integers.

\begin{array}{ccccccccccc} & &65 && \\ \times & & 535& & & & \\ \cline{3-5} & &325& & \\ & &195~~~& & \\ & &325~~~~~~~& & \\ \cline{3-5} & &347.75~~~~~~& & \\ \end{array}

The number of decimal places in 65 is 0 and the number of decimal places in 5.35 is two. Altogether there are 2 decimal places in both the factors. Hence, in the final answer, we will move the decimal point 2 points to the left. When we moved the decimal point two points to the left, we got the answer 347.75 kilometers.

 

Example 4

Ben completed his homework in 1 hour 45 minutes. His younger sister Anna took 2 times as many hours as Ben took to do his homework. How much time did Anna take to finish her homework?

Solution

If Ben took 1 hour 45 minutes to complete his homework, then Anna should complete her homework in 2 x (1 hour 45 minutes). 1 hour 45 minutes can be written in the decimal form as 1.45 hours. Let us calculate the time taken by Anna to complete her homework.

\begin{array}{ccccccccccc} & &1.45 && \\ \times & & 2& & & & \\ \cline{3-5} & &290& & \\ \cline{3-5} & &2.90& & \\ \end{array}

Since there was a total of 2 decimal places in the two factors altogether, therefore we have moved the decimal point two places to the left in the final answer. Hence, Anna took 2 hours 90 minutes to complete her homework. In decimal form, the time taken by Anna is written as 2.90.

 

Example 5

Solve 25.36 · 11.1.

Solution

We will eliminate the decimal points in both the factors and multiply them together as the normal integers.

\begin{array}{ccccccccccc} & &2536&& \\ \times & &1111& & & & \\ \cline{3-5} & &2536~~~& & \\ & &2536~~~~~~~& & \\ & &2536~~~~~~~~~~& & \\ \cline{3-5} & &281.496~~~~~~& & \\ \end{array}

Since there are two decimal places in the number 25.36 and one decimal place in the number 11.1, therefore altogether both the numbers have 3 decimal places. In the final answer, we will move the decimal point 3 places to the right. Hence, the final answer is 281.496.

 

Example 6

There are 5 boxes of salt in the kitchen. Each box has 2.15 kg of salt in it. How much salt is there altogether in 5 boxes?

Solution

The total amount of salt can be calculated by multiplying the number of boxes with the amount of salt in kgs. The amount of salt in kilograms is given in a decimal number, whereas the number of boxes is given in the form of a whole number. We will simply multiply the amount of salt and the number of boxes together to get the total amount of salt in all the five boxes.

Before multiplying, we will eliminate the decimal point from the number 2.72 and multiply it with 5 like integers.

 

\begin{array}{ccccccccccc} & &272&& \\ \times & &5& & & & \\ \cline{3-5} & &1360& & \\ \cline{3-5} & &13.60~~~~~~& & \\ \end{array}

Since the numbers 5 and 2.15 have 2 decimal places altogether, therefore we will move the decimal point two points to the left in the final answer. Hence, the five boxes have 13.60 kilograms of salt altogether.

 

 

Multiplying by the Unit Followed by Zeros

To multiply a number by a unit followed by zeros, move the decimal point to the right as many places as there are zeros in the unit. Let us consider the following examples which will make this concept more clear.

1. 1.236 . 10

As the decimal number 1.236 is multiplied by the unit followed by a single zero only, therefore we will move the decimal point one place to the right. The answer is 12.36.

2. 1.236 . 100

The number is multiplied by the unit followed by the two zeroes. Hence, we will move the decimal point 2 places to the right in the final answer. The final answer is 123.6.

3. 1.236 . 1000

The decimal number is multiplied by the unit followed by three zeroes. Therefore, we will move the decimal point three places to the right in the final answer. The final answer is 1236.

4. 1.236 . 10000

As the number is multiplied by the unit followed by four zeroes, therefore we will move the decimal point four places to the right. The final answer is 12360.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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