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Expertly multiply decimals by whole numbers or other decimals
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When you want to multiply any two numbers involving decimals, this process is called decimal multiplication. Multiplying decimals may look tricky, but all you have to do is follow a simple set of steps, and we're here to explain them. You can multiply two decimals together or multiply one decimal by a whole number—read on for a step-by-step guide for any decimal multiplication problem you’re looking to solve.
Steps
Section 1 of 4:
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Stack the numbers so that the one with the most digits is on top. Place one number on top of the other with a multiplication bar below them. For example, let’s say you’re multiplying .43 by .06. These numbers have the same number of digits, so you can stack them in any order. [1] X Research source
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Multiply the numbers as you would in ordinary multiplication. Ignore the decimals for now and multiply the numbers together as if they were whole integers. For example, you would follow these steps to multiple .43 and .06 as if they were whole numbers like 43 and 6: [2] X Research source
- Multiply the 6 in .0 6 by the 3 in .4 3 to get 18 .
- Write 8 below the rightmost column and carry the 1 on top of the leftmost column.
- Multiply the 6 in .0 6 by the 4 in . 4 3 to get 24.
- Add 24 to the 1 that was carried to get 25 .
- Write 25 to the left of the 8 under the multiplication line.
- When you start multiplying .43 by 0, you'll see that you only get 0, so there's no need to write anything down.
- The final product of this step (while ignoring decimal points) is 258 .
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Sum the combined number of digits on the right side of each decimal point. For example, there are two digits on the right side of the decimal point in .43 (4 and 3). There are also two digits on the right side of the decimal point in .06 (0 and 6). Add 2 and 2 (the number of digits for each decimal) to get 4—the total amount of numbers to the right of both decimal points. [3] X Research source
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Move the decimal point of the product to the left that number of times. Take the product you calculated in the previous steps and place a decimal on its rightmost end. In our working example, we would start with the decimal point at the end of the whole number 258 and move it over 4 times to the left. [4] X Research source
- The number 4 comes from the combined number of digits on the right hand side of our original decimals.
- The decimal point should end up one space past the 2 in 2 58.
- Fill in the empty space between the decimal and the 2 with a zero—this step is only necessary if there’s a blank space between the decimal point and the leftmost digit. [5] X Research source
- Therefore, the final product is .43 x .06 = .0258 .
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Check your work by dividing the answer by either decimal. Divide your final product by either one of the original decimals—if the answer is the other decimal, then your work has been done correctly.
- For example, you may want to check that .43 multiplied by .06 is indeed .0258.
- To do so, divide .0258 by .06. If you get .43, then your answer is correct!
- Alternatively, you could divide .0258 by .43. If you get .06, then your answer is also correct!
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Section 2 of 4:
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Stack the number with the most digits on top of the other number. Place both numbers on top of the multiplication line. If you’d like to multiply 1.21 by 3, for example, 1.21 will be on top because it has more digits.
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Multiply the numbers as if they were both whole numbers. Take away the decimal point for now, and multiply the two numbers together as if they were normal integers. For example, follow these steps to find the product of 1.21 x 3:
- Multiply the 1 in 1.2 1 by 3 to get 3 .
- Write 3 below the rightmost column.
- Multiply the 2 in 1. 2 1 by 3 to get 6.
- Write 6 below the middle column
- Multiply the 1 in 1 .21 by 3 to get 3.
- Write 3 below the leftmost column.
- The final product of this step (while ignoring decimal points) is 363 .
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Count the total number of digits on the right side of the decimal point in each number. For example, there are two digits on the right side of the decimal point in 1.21 (2 and 1). Our whole number (3) has no decimal point, so it has 0 digits to the right. Add 2 and 0 (the number of digits for each decimal) to get 2—the total amount of numbers to the right of both decimal points. [6] X Research source
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Shift the product’s decimal point to the left that number of times. Place a decimal on the rightmost end of the product you calculated in the previous steps. For the product 363 , for example, place the decimal point after the final 3, then move it 2 times to the left.
- We’re getting the number 2 from the combined number of digits on the right-hand side of the decimals in our original multiplication factors.
- The resulting product after moving the decimal point two spaces is 3.63 .
- Therefore, the final answer is 1.21 x 3 = 3.63 .
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Check your work by dividing the product by either original number. Divide your final answer by either one of the original multiplication factors—if the answer is the other factor, then your work has been done correctly.
- For example, you may want to check that 1.21 multiplied by 3 is indeed 3.63.
- To do so, divide 3.63 by 1.21. If you get 3, then your answer is correct!
- Alternatively, you could divide 3.63 by 3. If you get 1.21, then your answer is also correct!
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Section 3 of 4:
Solving a Decimal Multiplication Word Problem
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Create an equation that represents the word problem. Write out the situation presented in the word problem in mathematical terms. Let’s use this word problem as an example:
- Caitlin says that she has 2.2 times as many Instagram followers as Esther. If Esther has 43 Instagram followers, how many does Caitlin have?
- Solving this problem requires multiplying the decimal number 2.2 with the whole number 43.
- The mathematical equation for this problem would be 2.2 x 43 = ? .
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Stack the numbers with whichever has the most digits on top. Place both numbers on top of a multiplication line. In the example equation 2.2 x 43 = ? , 2.2 and 43 have the same number of digits so they can be stacked in any order.
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Multiply the numbers as if they were multi-digit whole integers. Ignoring the decimal point for now, multiply the double-digit numbers together as normal. In our example, the steps would proceed as follows:
- Multiply the 3 in 4 3 by the 2 in 2 2 to get 6 .
- Write 6 below the rightmost column.
- Multiply the 3 in 4 3 by the 2 in 2 2 to get 6 .
- Write 6 below the leftmost column
- Place a zero under your result in the rightmost column, directly under the 6.
- Multiply the 4 in 4 3 by the 2 in 2 2 to get 8 .
- Write 8 to the left of the 0 in the lowest row.
- Multiply the 4 in 4 3 by the 2 in 2 2 to get 8 .
- Write another 8 to the left of the one you wrote previously.
- Add 66 + 880 to get 946 .
- The final product of this step (while ignoring decimal points) is 946 .
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Count up the number of digits on the right side of each decimal point. For example, there’s one digit on the right side of the decimal point in 2.2 and no decimal points in the whole number 43. Add 1 and 0 to get 1—the total amount of numbers to the right of both decimal points. [7] X Research source
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Move the product’s decimal point to the left that number of times. Write a decimal point on the rightmost end of the product you calculated in the previous steps. With 946 , for example, place the decimal point after the 6 then move it one time to the left.
- The resulting product after moving the decimal point one place over is 94.6 .
- Therefore, the final answer is 43 x 2.2 = 94.6 .
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Write out your answer in a full sentence. Relate your product back to the original situation presented by the word problem. You can also round the number as needed for the answer to make sense—in this example, we'd round 94.6 to 95, since a person couldn't have 94.6 followers. Following our example, the final answer would read something like “Caitlin has 95 Instagram followers.”
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Worksheet & Answer Key
Expert Q&A
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QuestionHow do I round a decimal?Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration.To round a decimal, identify the desired place value and examine the digit to its right. If the digit is less than 5, round down; if it's 5 or greater, round up.
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QuestionWhat are decimal names?Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration.The positions to the right of the decimal point are assigned names that correspond to the place values of whole numbers. Consequently, the initial digit to the right of the decimal point denotes tenths, followed by hundredths, thousandths, and so forth. This naming convention facilitates a systematic understanding of the fractional components in decimal numbers.
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QuestionHow would I find the product of a number and a number with a decimal? Example, 12.5 x 16.DonaganTop AnswererMultiply normally, then count the total number of places to the right of the decimal point (in this case, one). Place the decimal point in the product by counting one place to the left of the right-most digit.
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Tips
- If you’re multiplying a decimal by 10, 100, or 1000, you simply have to shift the decimal point toward the right as many spaces as the number of zeros in the power of 10. If you multiply the decimal 2.32 by 100, for example, shift the decimal point two places to the right to get 232.Thanks
- Decimal multiplication follows the same steps as whole number multiplication, but you have to add the correct amount of decimal spaces at the end.Thanks
- You don’t have to line up the decimal points of the products—this is only necessary when subtracting or adding decimals .Thanks
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Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with Taylor Klein .
References
- ↑ http://www.math.com/school/subject1/lessons/S1U1L5GL.html
- ↑ https://www.mathsisfun.com/multiplying-decimals.html
- ↑ https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-multiplying-decimals/v/more-intuition-on-multiplying-decimals
- ↑ http://www.coolmath.com/prealgebra/02-decimals/08-decimals-multiplying-01
- ↑ https://www.mathsisfun.com/multiplying-decimals.html
- ↑ https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-multiplying-decimals/v/more-intuition-on-multiplying-decimals
- ↑ https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-multiplying-decimals/v/more-intuition-on-multiplying-decimals
- ↑ https://www.mathsisfun.com/multiplying-decimals.html
- ↑ https://www.mathsisfun.com/multiplying-decimals.html
About This Article
Article Summary
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To multiply decimals, line up the numbers vertically so that the decimal points are in the same position. Then, multiply as normal and temporarily ignore the decimal points. Once you have your answer, count how many numbers in each of the original factors are to the right of the decimal point. For example, 0.02 is 2 spots to the right of the decimal point. If you were multiplying 0.02 × 0.4, the total number to the right of the decimal point is 3. Take this total number and then move the decimal point in your answer by that number of spots. If you move the decimal point past the first number of the answer, add zeros after the decimal point until you reach the numbers. If you want to learn how to check your answer to see if it's correct, keep reading the article!
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