Dividing Decimals is similar to dividing whole numbers, except for the way we handle the decimal point. When we divide decimals, we change the divisor to a whole number by moving the decimal point all the way to the right. Then, we move the decimal point of the dividend up to the same number of places to the right, and divide the resultant numbers in the normal way as we do regular division.
Let us learn more about the division of decimals by reading the content given below, which will help us to understand this better.
|1.||What are Decimals?|
|2.||Dividing Decimals Definition|
|3.||Dividing Decimals Through Long Division|
What are Decimals?
Decimals are a part of the extended number system to express tenths, hundredths, thousandths, and so on. Working with decimals may seem a bit complex but the various operations using decimal numbers is quite similar to the operations using whole numbers. A decimal number has a whole number part and the fractional part separated by a dot. The digits following the decimal point show a value smaller than one.
For example, 24.15 is a decimal number with 24 in its number part and 15 in the decimal part. This can be understood with the following explanation: 24.15= 20 + 4 + 0.1 + 0.05.
Dividing Decimals Definition
The process of dividing decimals is similar to the normal division process, but we just need to keep in mind the decimal point which should be correctly placed in the quotient. Since we are referring to decimals, the following steps will help us to understand the process of dividing decimals.
- To divide a decimal number by a whole number, the division is performed in the same way as in the whole numbers. We first divide the two numbers ignoring the decimal point. Then, the decimal point in the quotient is placed in the same position as in the dividend. For example, 18.2 ÷ 2 = 9.1
- To divide a decimal number by a decimal number, multiply the divisor by as many tens as necessary until we get a whole number, and remember to multiply the dividend by the same number of tens. For example, 13.8 ÷ 0.6 becomes 138 ÷ 6 = 23.
Dividing Decimals by Whole Numbers: Dividing decimals by whole numbers is similar to the normal division. Here the dividend is a decimal and the divisor is a whole number, so the quotient will have the number of decimals based on the decimals in the dividend. The division of decimals with a whole number is easily done by taking the following steps.
- Step 1: For example to divide 78.92 ÷ 4, ignore the decimal and divide normally until you get 0 as the remainder.
- Step 2: Place the decimal point in the quotient in the same position as given in the dividend. 78.92 ÷ 4=19.73. Thus, we get 19.73 as the answer, where the decimal is placed according to the decimal of the dividend.
Dividing Decimals by another Decimal Number: In this division, both the dividend and the divisor are decimals and we can solve them by two methods. In the first method, we first move the decimals of the divisor to make it a whole number, and then we move the decimals of the dividend. Let us understand this with the help of the following steps:
- Step 1: For example, to divide 48.5 by 3.5, move the decimal of the divisor to the right as many times as necessary to make it a whole number. This makes the divisor 35.
- Step 2: Move the decimal in the dividend up to the same number of digits as you moved it in the divisor. This makes the divisor 485.
- Step 3: Now, divide the dividend (485) by the divisor (35) just like regular division.
The second method is used when the number of digits after the decimal in the dividend is more or less than the number of decimals in the divisor.
If the dividend's decimal place is more than or equal to the divisor's decimal place:
- Step 1: Ignore the decimal and divide normally until you get 0 as the remainder. For example, to divide: 0.09 ÷ 0.3, we ignore the decimals and write it as 9 ÷ 3= 3.
- Step 2: Place the decimal point using the formula: Dividend's decimal place - Divisor's decimal place= Quotient's decimal place. Now, using the formula, we get 2-1 =1. Hence, the decimal of the quotient will be placed as 0.3
If the dividend's decimal place is less than the divisor's decimal place: In this case, convert the decimal to a fraction. For example: 0.4 ÷ 0.02 = 4/10 ÷ 2/100 = 4/10 × 100/2 = 20
Dividing Decimals Through Long Division
The long division with decimals can be easily done just as the normal long division. The following sequence of steps explain the process of long division of decimals.
- First, write the division in the standard form. Start by dividing the whole number part by the divisor.
- Place the decimal point in the quotient above the decimal point of the dividend. Bring down the tenth digit.
- Divide and bring down the other digit in sequence. Divide until 0 is obtained in the remainder. Thus, the decimal in the quotient is similar is equal to the decimal in the dividend.
Now, let us look at the following tips that are helpful while dividing decimals.
- Convert the divisor to a whole number by multiplying by the powers of 10. Multiply the dividend by the same powers of 10.
- When you divide a decimal number by 10, move the decimal point to the left by one place.
- When you divide a decimal number by 100, move the decimal point to the left by two places.
- When you divide a decimal number by 1000, move the decimal point to the left by three places.
Example 1: Rishi has a collection of marbles that weigh 0.8 grams each. How many marbles does he have if their total weight is 376 grams?
Here, the weight of one marble is equal to 0.8 grams. The total weight of all the marbles together is equal to 376 grams. Thus, to find the number of marbles, we need to divide the total weight by the weight of one marble: 376 ÷ 0.8 = 376 ÷ 8/10 = 376 × 10/8 = 3760/8 = 470.
Therefore, Rishi has 470 marbles.
Example 2: Ishan wants to know the steps that need to be followed to find the result of 1.683 ÷ 0.09. Can you help him with the division?
Here are the steps Ishan needs to follow to find the result of 1.683 ÷ 0.09. First, the divisor is changed to a whole number 0.09 × 100 = 9, then the dividend is also multiplied with 100: 1.683 × 100 = 168.3. Now, the division is done in the following way.
Therefore, 1.683 ÷ 0.98 = 18.7
Example 3: Sohan used 337.7 kg of potatoes for making 5 batches of chips. How many did he use in one batch?
Solution: To calculate the quantity of potatoes that Sohan used in one batch, we need to divide the total quantity of potatoes by the number of batches. (337.7 ÷ 5)
On performing long division, we get 67.54. Therefore, Sohan used 67.54 kg of potatoes in each batch.
Practice Questions on Dividing Decimals
FAQs on Dividing Decimals
How do You Divide a Decimal By 100?
The decimal point of a decimal number moves by two places towards the left if we divide it by 100. For example, 34.286 ÷ 100 = 34.286/100 = 0.34286, and 678.37 ÷ 100 = 678.37/100 = 6.7837. Here, we move the decimal point of the dividend to the left by 2 places.
Why do You Move The Decimal When Dividing?
Decimals are the fractions that have the powers of 10 in the denominator. 8.9= 89/10. To divide decimal numbers we move the decimal places as many times to the left as many zeros are there in the denominator. For example, 67 ÷ 10 = 67/10 = 6.7, and 67 ÷ 100 =67/100 = 0.67, and 67 ÷1000 = 67/1000 = 0.067
How do you Calculate Decimals?
All the four operations of addition, subtraction, multiplication, and division are done in decimals in the same way as done with any other number system. For example: Addition: 12.7+2.8=15.5, Subtraction: 45.53-18.36=27.17, Multiplication: 2.4 × 5 =12, Division: 4.8 ÷ 0.4= 12
How do we Divide Decimals With Whole Numbers?
The division of a decimal with a whole number is the same as the normal division. The decimal is placed in the quotient according to the decimal of the dividend. Let us understand this with a simple example. The division of 42.7 by 7 gives 6.1.
Can a Decimal be a Whole Number?
Any number to the right of a decimal point has a value less than 1, so it cannot be a whole number. However, whole numbers like 5, 11, 22 can be written as decimal numbers such as 5.0, 11.0, 22.0.
What is the First Step in Dividing Decimals?
The first step in dividing decimals is to remove the decimals by multiplying or dividing with an exponent of 10. The possible exponents of 10 are 10, 100, 1000, and so on. Let us understand this with an example. For dividing 12.5 by 0.5, we have 12.5 ÷ 0.5 = (12.5 × 10) ÷ (0.5 × 10) = 125 ÷ 5 = 25. Thus, we first removed the decimals by multiplying the numbers by 10 and then the division was carried out.
What to do With a Remainder When Dividing Decimals?
When dividing decimals, the remainder is left aside as a decimal or a whole number. No further calculations are performed on the remainder. In perfect divisions, the remainder is a zero.
What is the Difference Between Multiplying and Dividing Decimals?
The multiplication and division of decimals involves shifting the decimal places in the answer. In multiplication, the number of decimal places is added in the resultant answer, and in the division, the number of decimal places is subtracted in the answer. To understand this let us take a simple example: 0.0020 × 0.005 = 0.0000100, and 0.0020 ÷ 0.005 = 0.4. Observing this we see that the division or the multiplication process is the same as the normal division or multiplication, but the decimals are added in multiplication, while the decimals are subtracted in the division.