When it comes to calculating, knowing how to multiply decimals is essential. Assume you have to give each youngster 0.25 of a chocolate bar, and there are a total of 12 children. How many chocolate bars do you think you need? To get the required quantity of chocolate bars, multiply 12 by 0.25. How do you do this? If you are unsure of how to multiply decimals, don’t worry because in this article we provide you with all the knowledge, examples, explanations, and solutions necessary.
What is decimal multiplication?
Decimal multiplication and whole number multiplication work in the same way but with an additional step. When multiplying decimals, you must note the number of digits there are after the decimal points as this number will indicate how many decimal places you need to include once you’ve completed the multiplication.
How to multiply decimals
Multiplying a Decimal with a Whole Number
The sole difference between multiplying decimals with whole numbers and multiplying whole numbers is the position of the decimal point. To multiply decimals with whole numbers, follow the steps below:
- Step 1: Remove the decimal to begin with, and multiply the two numbers as you otherwise would.
- Step 2: Add up the number of decimal places in the decimal numbers (e.g., 0.325 has 3 decimal places whilst 0.5 only has 1).
- Step 3: With your total number of decimals places, convert the product of the multiplication into a decimal. For example, if you have 3 decimal places and are converting 6792, the answer is 6.792. It’s that simple!
Let’s look at a real-world example of multiplying decimal values by whole numbers. A group of 15 students decided to donate to a relief fund. Each student contributed $ 6.5 to the cause. What was the total amount raised by the entire class? 15 students contributed a total of 6.5 x 15 = $97.5.
How did we get $97.5?
6.5 has 1 decimal place which we need to take note of as this means our answer will have one decimal place. Then we multiply the decimal by 10, 100, or 1000 to form a whole number – in this case, we multiply 6.5 by 10 to form 65.
Therefore, our new calculation is 65 x 15 = ?
To complete this we can break up the numbers into their place value digits and multiply them with each other:
- 60 x 10 = 600
- 60 x 5 = 300
- 10 x 5 = 50
- 5 x 5 = 25
Then we add all these up: 600 + 300 + 50 + 25 = 975
*Remember: since we multiplied 6.5 by 10 to form a whole number, we need to put that decimal place back in our answer, as such we divide 975 by 10 which equals $97.5.
Multiplying a decimal by 10, 100, or 1000
When multiplying by a power of 10, i.e., 10, 100, 1000, you simply move the decimal place to the right by the number of zeros. For instance, if you multiply a decimal by 1000 then you move the decimal place 3 times to the right.
Because there is one zero in the number 10, multiplying a decimal by ten shifts the decimal point one place to the right. We shift the decimal point two places to the right when we multiply any decimal by 100. In the same way, multiplying a decimal by 1000 shifts the decimal point three positions to the right, and so on.
For example:
- 2.32(10) = 23.2
- 2.32(100) = 232
- 2.32(1000) = 2320
H3: Multiplying a Decimal by a Decimal
This section will assist you in learning how to multiply two decimal integers. It’s the same as the process of multiplying a whole number, with the exception that we have to add the total number of decimal places in both numbers, which must equal the number of decimal places in the product. Follow the steps below to multiply two decimals:
- Step 1: Ignore the decimal point at first and multiply the two values as usual.
- Step 2: Count and add the total number of decimal places in both integers after multiplication. This is the total number of decimal places in the product received after multiplication.
- Step 3: After completing step 2, add a decimal point to the result.
For example:
Multiply 0.345 by 12.022
Both digits contain 3 decimal places, meaning the total number of decimal places will be 6.
Then we have to multiply each decimal to form a whole number:
- 0.345 x 1000 = 345
- 12.022 x 1000 = 12022
Then we can multiply these two together:
- 300 x 10,000 = 3,000,000
- 300 x 2000 = 600,000
- 300 x 20 = 6000
- 300 x 2 = 600
- 40 x 10,000 = 400,000
- 40 x 2000 = 80,000
- 40 x 20 = 800
- 40 x 2 = 80
- 5 x 10,000 = 50,000
- 5 x 2000 = 10,000
- 5 x 20 = 1000
- 5 x 2 = 10
Then we add all these up. It is worth saying that there is a visual way to convey this method of multiply numbers called the ‘box’ method:
| x | 10,000 | 2,000 | 20 | 2 |
| 300 | 3,000,000 | 600,000 | 6000 | 600 |
| 40 | 400,000 | 80,000 | 800 | 80 |
| 5 | 50,000 | 10,000 | 100 | 10 |
Once added up, these equal a whopping 4,147,590. However, we are not finished yet as we need to put the decimal places back in. If you recall, both digits contain 3 decimal places, meaning the total number of decimal places will be 6. This means we take the decimal place in 4,147,590 and move it 6 places to the left: 4,147,590.00 transforms to 4.147590.
Important Notes
Here are a few key rules and aspects of decimals to keep in mind when undertaking a multiplication with decimals:
- The process for multiplying decimals is the same as for multiplying whole integers.
- The decimal point should be put in the product so that the total number of decimal places in the product equals the sum of decimal places in all multiplicands and multipliers.
- When placing the decimal point, be careful to maintain all of the zeros in the product.
- The product’s trailing zeros can be removed.
Multiplying decimals examples
Question 1: Multiply 0.23 by 15
To begin we need to convert the decimal into a whole number by multiplying it by 100. Then we can calculate 23 x 15 so, using our box method:
- 20 x 10 = 200
- 20 x 5 = 100
- 3 x 10 = 30
- 3 x 5 = 15
Once added up, this equals 345, but the answer is not fully completed as we must insert our decimal place. Since we multiplied 0.23 by 100 to convert it to a whole number, we can divide 345 by 100 to insert our decimal place. This means 0.23 x 15 = 3.45!
Question 2: Multiply 0.21 by 0.3
This is interesting as the decimals have two different place values. 0.21 has hundredths whilst 0.3 only has tenths. Nevertheless, the method is the same. We begin by counting the place values – in this case it is 3. Then, we multiply the numbers as we normally would:
21 x 3 = 63
Since we have three place values, we need to move the decimal place to the left 3 times: 63.0 becomes 0.063!
Quick-fire Practice Questions
Try these quick-fire decimal multiplications:
- 2.5 x 10 = ?
- 0.0023 x 100 = ?
- 0.1 x 1000 = ?
- 0.2285 x 100 = ?
- 49.21 x 10 = ?
Here are the answers:
- 2.5 x 10 = 25
- 0.0023 x 100 = 0.23
- 0.1 x 1000 = 100
- 0.2285 x 100 = 22.85
- 49.21 x 10 = 492.1
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