Multiplying Decimals
Multiplying decimals is very important when we talk about the grouping of items. Suppose you have to distribute 0.25 part of a chocolate bar to each child and there is a total of 12 children. How many chocolate bars would you need? To find the number of chocolate bars required, we have to multiply 12 by 0.25.
Did you know that the history of decimals traces back to the ancient days in countries like China and India? Decimals were even adopted to the counting system by the Egyptians. By around 1500, almost all professional mathematicians accepted decimals and thus they became an integral part of the counting system around the world.
1.  How to Multiply Decimals? 
2.  Multiplying Decimals with Whole Numbers 
3.  Multiplying Two Decimals Numbers 
4.  FAQs on Multiplying Decimals 
How to Multiply Decimals?
Multiplying Decimals has the same procedure as that of multiplication of the whole numbers, except the placement of the decimal point in the product. In our everyday life, we have come across various instances where we have to use the multiplication operation on two numbers out of which at least one or both are decimal numbers. Imagine going out with your friend for lunch. You both order a platter costing $6.75 each. The total bill amounts to $15.75, including the taxes. To calculate the total cost of the platter in the bill, you need to multiply $6.75 × 2. Similarly, suppose you plan to gift your mother a flower bouquet on her birthday. Each flower costs $0.75 and you buy a total of 6 flowers. To find the total cost of the bouquet, you need to multiply $0.75 × 6. The above examples follow the application of multiplying decimals.
Multiplying Decimals with Whole Numbers
Multiplication of decimals with whole numbers is similar to the multiplication of whole numbers, the only difference being in the placement of the decimal point. The following steps can be followed to multiply decimals with whole numbers:
 Step 1: Initially, Ignore the decimal point and multiply the two numbers normally.
 Step 2: After multiplication, count the number of decimal places in decimal numbers. The product obtained after multiplication will have the same number of decimal places.
 Step 3: Place the decimal point in the obtained product following Step 2.
Let us understand a reallife situation where we multiply decimal numbers. A class of 15 students decided to contribute to a relief fund. Each student made a contribution of $6.5. What was the total amount collected from the whole class? Here, the contribution made by one student = $6.5. Total contribution made by 15 students = 6.5 × 15= $97.5.
Multiplying a decimal by Powers of 10
While multiplying any decimal by 10,100,1000, or any other power of 10, we just simply shift the decimal point towards the right as many places as the number of zeroes in the power of 10
 If we multiply any decimal by 10, we shift the decimal point one place towards the right, as there is 1 zero in the number 10
 If we multiply any decimal by 100, we shift the decimal point two places towards the right.
 Similarly, if we multiply a decimal by 1000, we shift the decimal point by three places towards the right, and so on.
For example, 2.32× 10 = 23.2, 2.32×100 = 232, 2.32× 1000= 2320.
Multiplying Two Decimals Numbers
This section will help you to learn about the multiplication of two decimal numbers. It is the same as that of the whole number, but the only difference is that in this we have to take the sum of the total number of decimal places in both the given numbers and that needs to be equal to the number of decimal places in the product. To multiply two decimals, follow the step listed below:
 Step 1: Initially, Ignore the decimal point and multiply the two numbers normally.
 Step 2: After multiplication, count the total number of decimal places in both the numbers combined. The product obtained after multiplication will have this total number of decimal places.
 Step 3: Place the decimal point in the obtained product following Step2.
Let us see the multiplication of two decimal numbers in the image given below:
Examples:
1. Multiply 0.567 and 13.065
Therefore, 0.567 × 13.065 = 7.407855. There are 6 digits after the decimal point.
2. Find the product of 16.45 and 8.5
Therefore, 16.45 × 8.5 = 139.825. The product has 3 digits after the decimal point.
Important Notes:
 The decimal multiplication follows the same procedure as the multiplication of whole numbers.
 The decimal point should be placed in the product in such a way that, the product has a number of decimal places equal to the sum of decimal places of all the multiplicands and the multipliers.
 Make sure you keep all the zeros in the product while placing the decimal point.
 If the product has more decimal places than the number of digits, zeros can be inserted before placing the decimal point in the product.
 The trailing zeros in the resultant product can be dropped.
Try and Solve these Challenging Questions:
 Charlie is paid $17.45 per hour and worked 42.5 hours last week. How much money did he earn last week (rounded to the nearest cent)?
 What is the total distance covered by a car if it traveled with a speed of 31.5 miles/hour for 7 hours and 15 minutes?
Solved Examples on Multiplying Decimals

Example 1: Rose is learning decimal multiplication. Can you help her multiply 0.6748 with 14.945?
Solution:
Let's see how to multiply 0.6748 and 14.945.
Note: The trailing zeros can be dropped. Therefore, 0.6748 × 14.945 = 9.944886

Example 2: Gracy went to the grocery store with her mother. Her mother bought 15 apples costing $1.25 each. Help Gracy to calculate the amount her mother needs to pay.
Solution:
We have Cost of one apple = $1.25. Thus, Cost of 15 apples = $1.25 × 15. Therefore, the cost of 15 apples is $18.75
Practice Questions on Multiplying Decimals
FAQs on Multiplying Decimals
How do you Multiply a Decimal Number by a Whole Number?
To multiply a decimal number by a whole number, follow the steps given below:
 Step1: Ignore the decimal point and multiply both the numbers.
 Step2: Count the number of decimal places in the decimal number.
 Step3: 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.
How do you Multiply Decimals by 1000?
To multiply decimals with 1000, shift the decimal point three places towards the right, as there are three zeroes in 1000.
How do you Teach Decimal Multiplication?
Let us see how to teach decimal multiplication to learners through the following ways:
 First, make students understand the meaning of decimal multiplication with the help of demonstration and visualization.
 Second, introduce the steps to multiply two decimal numbers to the students.
 Give practice questions.
What are the Four Rules of Decimals?
The four rules of decimals include different sets of rules for the operations of addition, subtraction, multiplication, and division.
Rules for Addition of Decimals
 All the decimal points should be lined up.
 Add trailing zeros wherever needed, to make all numbers have equal decimal places.
 Perform addition in a similar way to whole numbers.
 Simply move down the decimal point into your answer.
Rules for Subtraction of Decimals
 All the decimal points should be lined up.
 Add trailing zeros wherever needed, to make all numbers have equal decimal places.
 Perform subtraction in a similar way to whole numbers.
 Simply move down the decimal point into your answer.
Rules for Multiplication of Decimals
 Perform multiplication in a similar way to whole numbers.
 If the product has more decimal places than the number of digits, zeros can be inserted before placing the decimal point in the product such that only one zero will be there at the left of the decimal point and the decimal places in the product will be equal to the total number of decimal places in both the numbers.
 The decimal point should be placed in the product in such a way that, the product has a number of decimal places equal to the sum of decimal places of all the multiplicands and the multipliers.
 The trailing zeros in the fractional part of the resultant product can be dropped.
Rules for Division of Decimals
 The decimal point in the divisor should be moved towards the right to make it a whole number.
 Shift the decimal in the dividend to equal places towards the right.
 Perform division in a similar way to whole numbers.
 The decimal point needs to be moved to the same number of places in the quotient as the dividend.
How do you Multiply Decimals Less Than 1?
To multiply two decimals less than 1, follow the steps given below:
 Step1: Initially, Ignore the decimal point and multiply the two numbers normally.
 Step2: After multiplication, count the total number of decimal places in multiplicand and the multiplier combined. The product obtained after multiplication will have this total number of decimal places.
 Step3: Place the decimal point in the obtained product following Step2.
For example: 0.2 × 0.4 = 0.08
How do you Multiply Positive and Negative Decimals?
Positive and negative decimals are multiplied in a similar way as two decimals.
 Multiply both the numerical parts as we do in normal decimal multiplication.
 Since the product of one negative number and one positive number is negative, thus retain the negative sign before the numerical part of the product hence obtained.
For example, 0.5 × 0.3 = 0.15
What is a NonDecimal Number?
All the natural numbers without any fractional part are nondecimal numbers. For representing these we do not use a decimal point. Also, there is no tenth place or hundredth place in these numbers. For example 34, 5637, 8765, etc.