Multiplying decimals is a fundamental math skill that plays a crucial role in everyday calculations and various mathematical problems. Decimals are used to express the fractional part of integers. Multiplying decimals is similar to multiplication of integers we just need to take care of the placement of the decimal in the result. Some tricks and properties are associated with the multiplication of decimals, making multiplying them easier.
This article provides a complete guide on multiplying decimals, offering clear explanations, step-by-step instructions, and practical examples to enhance your understanding. Explore the tips and techniques to make multiplying decimals simple and straightforward, ensuring accuracy and confidence in your calculations.
What are Decimals?
Decimals are a way of representing numbers that are not whole. They use a decimal point to separate the whole number part from the fractional part. Decimals are based on the base-10 number system, which means each place value is a power of 10.
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How to Multiply Decimals?
Decimals are multiplied similarly to the multiplication of integer numbers with careful consideration of the placement of the decimal point in the product. Let us say that we have m digits after the decimal point in the first decimal number to be multiplied and n digits in the other decimal number, then after multiplying the numbers in the normal way, the decimal point is to be placed in such a manner that there are (m+n) digits after the decimal point.
For instance, we need to multiply 2.34 by 4.6, then we do get the product of 234 and 46 by normal multiplication as 10764 and place the decimal point such that there are 3, i.e. (2+1) digits after the decimal point. Thus, we get the final result of 10.764.
Steps to multiply a decimal with other numbers including decimals
Step 1: Ignore the Decimals: Temporarily ignore the decimal points and multiply the numbers as if they were whole numbers.
Step 2: Multiply the Numbers: Perform the multiplication as you normally would with whole numbers.
Step 3: Count the Decimal Places: Count the total number of decimal places in both of the original decimal numbers.
Step 4: Place the Decimal Point: In the product, place the decimal point so that it has the same number of decimal places as the total you counted in the previous step.
When the decimal numbers are multiplied, those powers of 10 get added and we get the required result as discussed above. The multiplication of decimal numbers with whole numbers is discussed below.
Multiplying Decimals with Whole Numbers
When a decimal number is multiplied by a whole number, the numbers are multiplied without consideration of the decimal point. After getting the result, the decimal point is placed as it was in the decimal number, i.e. if the decimal number had n digits after the decimal point, then the result obtained will also have n digits after the decimal point.
For instance, if 3.468 is to be multiplied by 8, we multiply 3468 with 8 in the normal manner to get 27744 and the decimal point will be placed in such a way that there are 3 digits after the decimal point as it was in the decimal number and obtain the final result as 27.744.
Multiplying Decimals with 10, 100, 1000 or any Power of 10
Multiplication of decimals with multiples of 10 is a special case of multiplying decimals with whole numbers. If a decimal number is multiplied with nth power of 10, then the decimal point shifts to right by n digits in the number.
For instance, we have 4.682 as the sample decimal number, then if it is multiplied by 10, we get 46.82 by shifting the decimal point towards right by one place. Similarly, if the decimal is multiplied with 100, we get 468.2 and if multiplied with 1000, we get 4682 by shifting the decimal point by 2 and 3 places respectively.
Multiplying decimals by powers of 10 (such as 10, 100, 1000, etc.) is a straightforward process. To multiply follow the steps added below:
Step 1: Identify the Power of 10: Determine how many places you need to move the decimal point based on the power of 10.
Step 2: Move the Decimal Point: Move the decimal point to the right by the number of places indicated by the power of 10.
Step 3: Add Zeros if Necessary: If you move the decimal point past the digits, add zeros to fill in the spaces.
For example, Multiplying 3.4567 by 103
Identify the Power of 10: 103, so move the decimal point three place to the right.
Move the Decimal Point: 3.4567 becomes 3456.7
So, 3.4567 × 103 = 3456.7
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Examples on Multiplying Decimals
1: Multiply 3.2 with 6.84.
Here, we see that the numbers to be multiplied are decimal numbers.
Digits after decimal point in 3.2 is 1 and that in 6.84 are 2. So, in the final result of multiplication of decimal numbers, there would be 3, i.e. (2+1) digits after the decimal point.
First, we multiply 32 and 684 to get the product as 21888.
Now, we need to place the decimal point in such a way that there are 3 digits after the decimal number.
We get the final result as 21.888 for the multiplication of 3.2 and 6.84.
2: Multiply 6.4 by 8.
Here, we have a decimal number and a whole number to be multiplied. So, in the final result of multiplication, we will have same number of digits after the decimal point as in the decimal number.
We do the normal multiplication of 64 and 8 to get 512, and place the decimal point such that there is one digit after the decimal as it was in the decimal number.
Hence, the final result is obtained as 51.2.
3: Multiplying 123.47 by 104
Identify the Power of 10: 104, so move the decimal point four place to the right.
Now but in given decimal we have only two places after decimal so we will add two zeros after the end, i.e. 123.4700 is new number
Move the Decimal Point: 123.4700 becomes 1234700
So, 123.47 × 104 = 1234700
4: Multiplying 89.89 by 10
Identify the Power of 10: 101, so move the decimal point one place to the right.
Move the Decimal Point: 89.89 becomes 898.9
So, 89.89 × 10 = 898.9
Multiplying Decimals - Practice Questions
1. Multiply 6.7 by 3.268.
2. Multiply 7.45 by 5.
3. An item costs 4.5 rupees each. What would be the cost for 7 such items.
4. Milk costs 60 rupees per litre. Find the cost for 2.5 litres of milk.
5. Give the result of multiplication of 4.56 and 7.24.