Step-by-Step Guide: How to Divide to Decimal Places
Long division is the process of dividing large numbers into steps or parts, dividing the problem into a sequence of easier steps. Long division to decimal is similar to the long division to whole numbers, except for the way we manage the decimal point. The secret to performing long division to decimal places is to add zeros after the decimal point. For example, 140 is the same as 140.00. We can include as many zeroes as we wish after the decimal point without changing the value of the number.
Let us learn more about how to do the long division with decimals by reading the content given below, which enables us to understand better.
Long Division to Decimal Steps
Long division to decimal can be easily done just as the normal long division. The following steps explain how to do long division with decimal points.
Step 1: The first step is to write the number in standard form. Start by dividing the whole number part by the given divisor.
Step 2: Place the decimal point in the quotient above the decimal point of the dividend. Bring down the tenth digit for continuing the further division process.
Step 3: Divide and bring down the other digits such as hundredths, thousandth, etc in a sequence. Divide until you get the 0 in the remainder. Hence, you will find the same number of decimal points are placed in the quotient as in the dividend
Long Division to Decimal When Divisor is Not a Whole Number
The following steps with example explain long division to decimal when the divisor is not a whole number:
Divide 16.9 by 6.5
1. As the divisor is not a whole number, we will move the decimal point to the right side to convert it into a whole number and also move the decimal point in the dividend one place to the right as shown below.
2. Divide usually as a whole number. The divisor 65 goes into the dividend 139, 2 time(s), with 39 left as a remainder.
3. To continue the division process, add zero to the right of the decimal point in the dividend. Further, bring down the 0 and place it to the end of 39, making it 390.
4. 65 goes into the 390, six times with a remainder of 0. We will write 6 in the quotient just above the zero and place the decimal point in the quotient above the decimal point of the dividend as shown below.
Hence, 16.9 when divided by 6.5 gives a quotient of 2.6 and remainder 0.
Long Division 3 Examples With Solutions
1. Hitesh Wants to Know the Long Division Steps that Need to be Followed to Obtain the Result of 1.683 ÷ 0.09. Can You Help Him to Find the Result?
Solution:
Following are the steps that Hitesh needs to follow to get a result of 1.683 ÷ 0.09.
First, the divisor will be converted into the whole number by multiplying the divisor by 100 (0.09 100 = 9). Further, we will also multiply the dividend by 100 (1.683 100 = 168.3) to get the decimal point in the same number of places.
Now, the division will be performed in the following way:
Hence, 168.3 0.09 = 18.7
2. Ronak Distributed 75 Chocolates Among 3 of his Friends. How Many Chocolates Did he Distribute to Each Friend?
Solution:
Total Number of Chocolates = 75
Number of Friends = 3
To find the number of chocolates distributed to each friend, we have to divide 75 by 3 because an equal number of chocolates are distributed to each friend.
Hence, the number of chocolates distributed to each friend is 25.
Points to Remember
There is a certain procedure of dividing the decimals by the whole number.
The first step is to write the division expression in a completely standard form.
Then the decimal’s whole number has to be divided by the divisor.
The decimal point has to be placed above the quotient above the dividend’s decimal point and bring down the tenth digit.
Write 0 in the quotient in front of the tenth digit if the tenth digit of the dividend is not divisible by the divisor.
In order to attain 0 in the reminder, zeros must be added to the dividend, if not required then proceed as usual.
Dividing a decimal by 10 will move the decimal point to one place towards the left,
In order to Divide 5 by 100, place the decimal point in the numerator like 5/100 = 0.05. It will mean that the decimal point will shift to the left by two places since 100 has two 0’s.
Dividing 31 by 100 where it is written as 31/100, the denominator has two 0’s which is why the decimal point has to be placed in two places like 0.31.
Dividing decimals is like dividing whole numbers where the decimal point has to be taken into account along with its placement.
It has two ways for dividing, namely, dividing decimals by whole numbers or division of decimals by another decimal number.
Decimals may also be divided by 10, 100, and 1000.
There are certain rules that are to be followed during the division of decimals.
A division expression has four parts namely, dividend, divisor, quotient, and remainder.
Tips to Master this Chapter Like a Pro
Students can find this topic hard to understand and get confused with the basic concepts. In order to avoid such inconveniences, here are some quick ways to master Long Division to Decimals like a pro–
Always make notes.
Yes. Making notes can come in handy at any hour before the final exams. Long Division to Decimal places is diversified and the steps have to be revised regularly so a student does not forget the concepts of this topic.
Test after doubt clearing.
Students must test their knowledge after clearing their doubts in order to know if they have more doubts and understand their grasp on this topic. It is always better to make mistakes before exams and not in the exams.
Participate in online classes for Long Division to Decimal places.
Students must participate actively in interactive online classes to develop a sound understanding and sharpen their knowledge regarding this topic. Vedantu offers online classes that help students enhance their knowledge regarding Accounting Information Systems.
Understanding ‘Why’
Every knowledge that is perceived has to be questioned for a rational understanding of the topic. What are different terms that are used in the long division method? What is the process of the long division method? Such questions will help a student memorize this topic in a better way and with a deeper understanding.
Make sure all the questions in the textbook are answerable.
A student must be able to answer most of the questions present in the textbook. Struggling with questions will make a student unsure of the concepts and it will greatly impact the exams.
Solving sample papers on Long Division
For a better grip on this vast topic, a student must solve the sample questions aside from the questions present in the textbook. Not knowing how to answer any possible question on this topic can cause a student to panic during exams.
Solving questions from RD Sharma
Students must be willing to solve questions from the RD Sharma textbook for a better understanding of the possible questions that might be asked in the exams. The solutions to the questions presented in the RD Sharma textbook are available on Vedantu’s official website.
In totality, it is imperative that a student remains in touch with this chapter and begins to work from the first day. It is not tough with correct work and guidance. Vedantu offers online classes for clearing doubts and live sessions for a better understanding of this topic. Vedantu offers study materials according to the latest syllabus of the boards so that students don’t feel demotivated for the exams. A student can also download the solutions to the question related to Long division to Decimal places from Vedantu’s official website.
FAQs on Long Division to Decimal Places Made Easy
1. What is the main purpose of using long division to find decimal places?
The main purpose of using long division to find decimal places is to get a more precise answer when a number cannot be divided evenly. Instead of leaving a remainder, this method allows you to continue dividing to find the exact value in tenths, hundredths, and so on. It is essential for converting fractions into decimals and solving problems involving measurements or money.
2. What are the key terms to know for long division with decimals?
The key terms used in any long division problem are:
- Dividend: The number that is being divided.
- Divisor: The number you are dividing by.
- Quotient: The result or answer of the division.
- Remainder: The amount left over after dividing. In decimal division, we aim to make the final remainder zero by adding decimal places.
3. How do you correctly place the decimal point in the quotient during long division?
Placing the decimal point is a crucial step. The rule is simple: place the decimal point in the quotient directly above the decimal point in the dividend. Once you place it, you can ignore it and continue the division process as you would with whole numbers, bringing down digits (including added zeros) one at a time.
4. What is the step-by-step process for long division when dividing a whole number by a larger whole number (e.g., 5 ÷ 8)?
To divide a whole number by a larger one and get a decimal answer, follow these steps:
- Set up the long division with the smaller number as the dividend (inside) and the larger number as the divisor (outside).
- Since the divisor cannot go into the dividend, place a decimal point in the quotient above the dividend.
- Add a zero to the right of the dividend (e.g., 5 becomes 5.0).
- Now, divide as usual. Continue adding zeros to the dividend to bring down and keep dividing until the remainder is 0 or you reach the desired number of decimal places.
5. How do you perform long division if the dividend is a decimal but the divisor is a whole number (e.g., 12.5 ÷ 5)?
This is one of the most straightforward types of decimal division. First, place the decimal point in the quotient directly above the decimal point in the dividend. After that, you simply perform the long division as if there were no decimals involved at all. The presence of the decimal in the dividend only determines its position in the answer.
6. Why do we add zeros to the end of the dividend after the decimal point?
We add zeros after the decimal point in the dividend to continue the division process when we have a non-zero remainder. Adding zeros to the right of a decimal point does not change the value of the number (for example, 25 is the same as 25.0 or 25.00). This allows us to break down the remainder into smaller parts—tenths, hundredths, etc.—and find a more precise quotient instead of stopping with a remainder.
7. What is the difference between getting a remainder and finding a decimal answer?
A remainder is a whole number left over when a division is incomplete. For example, 13 ÷ 4 is 3 with a remainder of 1. A decimal answer is a more precise result obtained by continuing to divide that remainder. Instead of stopping, you add a decimal point and zeros to the dividend, effectively dividing the 'leftover' part into smaller fractional pieces. So, 13 ÷ 4 becomes 3.25, which is the exact answer.
8. How does the long division process change if both the dividend and the divisor are decimals (e.g., 7.82 ÷ 0.2)?
When the divisor is a decimal, you must first convert it into a whole number. To do this, shift the decimal point in the divisor to the right until it's a whole number. You must then shift the decimal point in the dividend by the same number of places to the right. For 7.82 ÷ 0.2, you move the decimal one place in both numbers, making the new problem 78.2 ÷ 2. After this adjustment, you can proceed with the division as you normally would.
9. Can you provide a real-world example of when long division to decimal places is used?
A common real-world example is splitting a bill among friends. If a pizza costs ₹955 and 4 friends want to share the cost equally, you would calculate 955 ÷ 4. Using long division, you would find that each person needs to pay ₹238.75. Without dividing to two decimal places, you wouldn't be able to determine the exact amount in rupees and paise.
10. What happens in long division if the numbers never result in a zero remainder?
If the division process continues indefinitely without the remainder ever becoming zero, you have a non-terminating decimal. These often have a repeating pattern of digits. For example, when you calculate 10 ÷ 3, the result is 3.333..., where the digit '3' repeats forever. In such cases, you typically round the answer to a specified number of decimal places, like two or three, depending on the requirement of the problem.
