How to Divide Decimals by Decimals? An easy approach
- Author: Noreen Niazi
- Last Updated on: December 15, 2023
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As someone who has taught math for years, I know many students struggle with dividing decimals by decimals. This skill is essential for doing higher-level math, and it’s important to master it early on. In this article, I will walk you through dividing decimals by decimals, including understanding place value, using the long division method, dealing with repeating decimals, and checking your answers. By the end of this article, you’ll have a solid grasp of how to divide decimals by decimals.
Understanding Place Value in Decimals
Before diving into dividing decimals by decimals, it’s important to have a solid understanding of place value in them. Each digit has a place value in a decimal number based on its position relative to the decimal point. The digit immediately to the left of the decimal point represents the one’s place, the digit to the left represents the tens place, and so on. To the right of the decimal point, the first digit represents tenths, the second digit represents hundredths, and so on.
When dividing decimals by decimals, it’s important to keep track of the place values of each digit. The number being divided (the dividend) should have the same number of decimal places as the divisor. If it doesn’t, you’ll need to add zeros to the end of the dividend until it does. For example, if you’re dividing 3.14 by 0.2, you’ll need to add a zero to the end of 3.14 to make it 3.140.
The Long Division Method for Dividing Decimals by Decimals
The long division method is the most common way to divide decimals by decimals. It’s the same method you learned for dividing whole numbers, but with a few extra steps. Here’s how it works:
- Write the divisor (the number you’re dividing by) outside of the division bracket and the dividend (the number you’re dividing) inside the bracket.
- If the dividend doesn’t have the same number of decimal places as the divisor, add zeros to the end of the dividend until it does.
- Divide the first digit of the dividend by the divisor. Write the quotient (the answer) above the division bracket, and write the remainder (what’s left over) to the right of the dividend.
- Bring down the next digit of the dividend and add it to the remainder. This gives you a new number to divide by the divisor.
- Repeat steps 3 and 4 until you’ve divided to the end of the dividend.
Let’s look at an example. Suppose we want to divide 12.6 by 0.3. Here’s how we would do it using the long-division method:
- We start by writing the divisor (0.3) on the outside of the bracket, and the dividend (12.6) on the inside. We then divide the first digit of the dividend (1) by the divisor:
- We write the quotient (0.9) above the division bracket, and the remainder (0.3) to the right of the dividend. We then bring down the next digit of the dividend (2) and add it to the remainder (0.3 + 2 = 2.3):
- We bring down the next digit of the dividend (6) and add it to the remainder (1.4 + 6 = 7.4):
- We divide 5 by the divisor to get 16. We’ve now divided all the way to the end of the dividend, so our final answer is 42.
Dividing Decimals with Repeating Decimals
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Sometimes when you divide decimals, you end up with a repeating decimal. This is a decimal that has a pattern that repeats infinitely. For example, when you divide 1 by 3, you get 0.333333… (with the 3s repeating forever). When dividing decimals with repeating decimals, you need to take a few extra steps.
- First, you’ll need to identify the repeating pattern. You can do this by looking for a sequence of repeated digits. For example, in 0.333333…, the repeating pattern is 3.
- Next, you’ll need to put a bar over the repeating pattern. This indicates that the pattern repeats infinitely. For example, 0.333333… can be written as 0.3̅.
- Finally, you’ll need to use long division to divide the decimals as usual. However, when you get to a point where you have a remainder that’s the same as the divisor, you know that the pattern will repeat. At this point, you’ll need to add a zero to the end of the remainder and continue dividing.
For example, suppose we want to divide 1.6 by 0.3. Here’s how we would do it:
- We start by dividing the first digit of the dividend (1) by the divisor (0.3):
- We write the quotient (0.5) above the division bracket and the remainder (0.1) to the right of the dividend. We then bring down the next digit of the dividend (6) and add it to the remainder (0.1 + 6 = 6.1):
- We divide 1 by the divisor (0.3) to get 3. We write this above the division bracket. We then subtract 3 times the divisor (0.3 x 3 = 0.9) from the dividend (6.1 – 0.9 = 5.2):
- We divide 5 by the divisor to get 16. We then bring down the next digit of the dividend (0) and add a zero to the end of the remainder (0.2 x 10 = 2). We now have 2 as our new dividend:
- We divide 3 by the divisor to get 10. We bring down the next digit of the dividend (0) and add a zero to the end of the remainder (0.5 x 10 = 5). We now have 5 as our new dividend:
- We divide 2 by the divisor to get 6. We’ve now divided all the way to the end of the dividend, so our final answer is 5.3̅.
How to Check Your Answer When Dividing Decimals by Decimals
When you’ve finished dividing decimals by decimals, checking your answer is important to ensure it’s correct. There are a few different ways to do this.
First, you can multiply the quotient (the answer you got) by the divisor (the number you were dividing by), and then add any remainder you had. The result should equal the dividend (the number you started with). For example, if you divided 12.6 by 0.3 and got a quotient of 42, you would multiply 0.3 x 42 to get 12.6.
Another way to check your answer is to work backward from the answer. Start with the quotient and multiply it by the divisor. Then, add any remainder you had. The result should be equal to the dividend. For example, if you divided 12.6 by 0.3 and got a quotient of 42, you would multiply 42 x 0.3 to get 12.6.
Real-World Applications of Dividing Decimals by Decimals
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Dividing decimals by decimals has many real-world applications. For example, if you’re a chef, you should divide a recipe for 1.5 cups of flour by 3 to make a smaller batch. If you’re a carpenter, you should divide a length of wood that’s 2.4 meters long into pieces that are 0.3 meters long. If you’re a scientist, you should divide a volume of liquid that’s 1.8 liters by 0.2 to figure out how many doses of a medication to give.
Common Mistakes to Avoid When Dividing Decimals by Decimals
Students make a few common mistakes when dividing decimals by decimals. One of the most common is forgetting to add zeros to the end of the dividend when it doesn’t have the same number of decimal places as the divisor. Another common mistake is forgetting to bring down the next digit of the dividend when you’re doing long division. It’s also important to keep track of each digit’s decimal point and place values.
Using Technology to Divide Decimals by Decimals
While it’s important to know how to divide decimals by decimals by hand, there are also many tools and resources available to help you. For example, you can use a calculator to divide you. Many online resources provide practice problems and step-by-step instructions.
Practice Problems for Dividing Decimals by Decimals
To help you practice dividing decimals by decimals, here are a few problems to try:
- 0.8 ÷ 0.2 =
- 3.9 ÷ 0.3 =
- 0.6 ÷ 1.2 =
- 6.2 ÷ 0.4 =
- 1.2 ÷ 0.8 =
Conclusion and Summary of Key Takeaways
Dividing decimals by decimals can be a challenging skill to master, but it’s essential for doing higher-level math. By understanding place value, using the long division method, dealing with repeating decimals, and checking your answers, you can become proficient at dividing decimals by decimals. Remember to avoid common mistakes, use technology when necessary, and practice, practice, practice. With these tools and strategies, you’ll be able to tackle any problem that comes your way.