How to Divide a Decimal by a Decimal: Step-by-Step Examples
Keeping the decimal point in mind, dividing decimals is similar to dividing entire numbers. Although there are specific guidelines to follow when splitting decimal numbers, the fundamental division procedure is the same. In this article, we will discuss long division with decimals, dividing decimals with whole numbers, and dividing decimals with other decimals.
Division of Decimal by Decimal
When dividing decimals, we must move the decimal point to the right in order to change the divisor to a whole number. The decimal point of the dividend is then moved the same number of places to the right, and the numbers that result are divided in the same manner as conventional long division.
Let us move one space for both:
6.4/0.4 is exactly the same as 64/4 as we did the move for both numbers. Refer to the following diagram.
How to Divide Decimals
Now we can calculate: 64/4=16
So the answer is: 6.4/0.4=16
How to Divide Decimal Numbers
To multiply one decimal by another:
The divisor's decimal point should be moved to the right until a whole number is reached.
To convert the divisor to a whole number, move the dividend's decimal point right by the same amount of spaces as the decimal point was moved.
Divide the new dividend by the new divisor after that.
The divisor should be multiplied by as many 10s as necessary to make it a whole number.
The dividend should be multiplied by the same amount of 10s.
Let’s understand it more clearly by dividing 4.2625 by 0.05.
Step 1: Write the number in fraction form like denominator and numerator.
Step 2: As we need to make the 0.05 as 5 we need more two decimals towards the left it will become then 5.00 which is 5. As we are changing the denominator we need to move two decimals from the numerator it will become from 4.2625 to 426.25
Step 3: Divide the 426.25 by 5.
Refer to the following Diagram.
How to Divide Decimals
Decimal Division by 10, 100, and 1000
Let's calculate the decimal division of a number by 10, 100, and 100
Think about \[{\rm{97}}{\rm{.5 }} \div 10 = 9.75\]. The decimal point has moved (to the left) in the quotient, but the digits in 97.5 and 9.75 are the same, i.e., 9, 7, and 5. As a result, when dividing a decimal by 10, the decimal point will move one place to the left because there is only one zero over one in 10.
From the previous illustration, we may understand that when decimals are divided by 10, 100, or 1000, the number and quotient digits will match. The decimal point in the quotient, however, is shifted to the left by an amount equal to the number of zeros above 1.
Conclusion
The decimal point must be moved to the right when dividing decimals in order to convert the divisor to a whole number. The numbers that result are split using traditional long division after the decimal point of the dividend is moved the same number of places to the right.
Decimal by Decimal Solved Examples
Example 1: Divide 8.91 by 2.2
By doing the long division method, we will get
The dividend is set at 8.91 and Divisor is 2.2
By moving the decimal point one place to the right, you may now convert the divisor 2.2 to a whole number. Next, move the decimal point one place to the right, keeping the same spacing, in the dividend.
\[8.91 \div 2.2 = 8910 \div 22\]
Divide 8.91 by 2.2.
Example 2: How are decimals divided into steps?
Following is a step-by-step process for dividing decimals by whole numbers:
teSp 1: Write the division numbers in a sequence.
Step 2: The decimal number's whole number component must now be divided by the divisor.
Step 3: After placing the quotient's decimal point above the dividend's decimal point, bring the tenth digit down.
Step 4: Enter 0 in the quotient and in front of the tenth digit if the acquired dividend's tenth digit cannot be divided by the divisor. If not, continue with the division process.
Step 5: Carry on with the previous step, adding zeros to the left number until the remainder equals zero.
Example 3: How to divide any number by 10?
The decimal point should be one place to the left when dividing a decimal number by 10. For instance, we may easily divide 12.87 by 10 by moving the decimal point to the left, yielding the result of 1.287.
FAQs on Division of Decimal by Decimal: Complete Guide
1. What is the basic rule for dividing a decimal number by powers of 10, like 10, 100, or 1000?
To divide a decimal number by a power of 10, you simply move the decimal point to the left. The number of places you move the decimal is equal to the number of zeros in the power of 10. For instance, to divide by 10 (one zero), you move the decimal one place to the left. To divide by 100 (two zeros), you move it two places to the left.
2. What is the method for dividing a decimal by another decimal number?
The primary goal is to make the divisor (the number you are dividing by) a whole number. This is done by following these steps:
Step 1: Count the number of decimal places in the divisor.
Step 2: Move the decimal point in both the divisor and the dividend to the right by that same number of places. This is equivalent to multiplying both numbers by a power of 10.
Step 3: Place the decimal point in your answer (the quotient) directly above the new position in the dividend.
Step 4: Divide as you would with whole numbers.
3. Can you provide a step-by-step example for dividing a decimal by a decimal, like 6.25 ÷ 0.5?
Certainly. To solve 6.25 ÷ 0.5, we follow the standard method:
First, we make the divisor (0.5) a whole number by moving its decimal one place to the right, making it 5.
Next, we must do the same for the dividend (6.25). We move its decimal one place to the right, making it 62.5.
The problem now becomes 62.5 ÷ 5.
Now, perform the long division. The decimal point in the quotient will be placed directly above the decimal in 62.5. The result is 12.5.
4. Why does the answer to a decimal division problem, like 0.8 ÷ 0.2, sometimes result in a whole number that is larger than the original decimals?
This happens because division is not just about splitting a number; it's about finding out how many times the divisor can fit into the dividend. In the example 0.8 ÷ 0.2, you are asking, "How many times does 0.2 fit into 0.8?" Since 0.2 + 0.2 + 0.2 + 0.2 = 0.8, we can see that 0.2 fits into 0.8 exactly 4 times. The result, 4, is a whole number and is larger than both 0.8 and 0.2.
5. How is the division of decimals used in real-life situations? Can you give an example?
Division of decimals is very common in everyday life. Here are a few examples:
Splitting Costs: If a restaurant bill of ₹1250.75 is split among 5 friends, you would calculate 1250.75 ÷ 5 to find each person's share, which is ₹250.15.
Calculating Fuel Mileage: If your car travels 450.5 kilometres on 20.2 litres of petrol, you can calculate the mileage by dividing 450.5 by 20.2.
Unit Pricing: To find the better deal at a supermarket, you can calculate the price per unit. For example, if a 2.5 kg bag of sugar costs ₹112.50, the price per kg is 112.50 ÷ 2.5, which is ₹45 per kg.
6. What is the logical difference between dividing 8.4 by 0.4 and dividing 84 by 4?
Logically, there is no difference in the final result because they represent the same mathematical ratio. To solve 8.4 ÷ 0.4, the first step is to make the divisor (0.4) a whole number. We do this by multiplying it by 10. To keep the problem equivalent, we must also multiply the dividend (8.4) by 10. This transforms the problem from 8.4 ÷ 0.4 into 84 ÷ 4. Both calculations will give the answer 21. The first form is simply the decimal representation of the same division problem.
7. What is the most common mistake students make when dividing a decimal by another decimal?
A very common mistake is only moving the decimal in the divisor but not in the dividend. It is essential to remember that to keep the equation balanced, whatever you do to the divisor, you must also do to the dividend. Forgetting to move the decimal in the dividend by the same number of places will lead to an incorrect answer. Another frequent error is misplacing the decimal point in the final answer (quotient).
