Dividing Decimals

Dividing Decimals is similar to dividing whole numbers, keeping in mind the position of the decimal point. While dividing decimal numbers, we need to follow a certain set of rules but the basic process of division remains the same. Let us learn how to divide decimal numbers, long division with decimals, how to divide decimals with whole numbers, and how to divide decimals with decimals in this article.

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. A decimal number has a whole number part and a fractional part separated by a dot which is the decimal point. The digits after the decimal point have a value smaller than 1. For example, 24.15 is a decimal number in which 24 is the whole number part and 15 is the fractional part. For dividing decimal numbers, we can come across 2 scenarios - one in which we need to divide decimals by a whole number, and the other in which we divide decimals by decimals. Let us read more about this in the following sections.

Dividing decimals by whole numbers is similar to normal division. Here, the dividend is a decimal number and the divisor is a whole number, so the decimal point in the quotient will be placed according to the decimal point of the dividend. We can understand this with the help of the long division of decimals.

Long Division of Decimals

The long division of decimals can be easily done like the normal long division. Let us understand this using an example.

Example: Divide 338.56 ÷ 23

Solution:

• Step 1: First, write the division in the standard form. Start by dividing the whole number part by the divisor.
• Step 2: Place the decimal point in the quotient above the decimal point of the dividend. Bring down the tenth digit.
• Step 3: Divide and bring down the other digit in sequence. Divide until 0 is obtained in the remainder. Thus, the decimal in the quotient is placed according to the decimal in the dividend.

Now, let us learn how to divide decimals by decimals.

For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division. Let us understand the conditions and rules for this method using an example.

Example: Divide 48.65 ÷ 3.5

Solution: In this division, the dividend and the divisor are decimals, so we need to convert the divisor to a whole number using the following steps.

• Step 1: The dividend is 48.65 and the divisor is 3.5. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 3.5 × 10 = 35.
• Step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 48.65 × 10 = 486.5. In other words, we need to move both the decimal points to the right until the divisor becomes a whole number.
• Step 3: Now, we have 486.5 as the dividend and 35 as the divisor. This can be divided as we do the usual division and we get 13.9 as the quotient.

Important Tips on Dividing Decimals

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.
• In order to divide a decimal number by 10, move the decimal point to the left by one place. For example, if we need to divide 45.67 ÷ 10, then it can be easily done by shifting the decimal point to the left and the answer will be 4.567
• In order to divide a decimal number by 100, move the decimal point to the left by two places. For example, if we need to divide 324.6 ÷ 100, then it can be easily done by shifting the decimal point to the left and the answer will be 3.246
• In order to divide a decimal number by 1000, move the decimal point to the left by three places. For example, if we need to divide 8934.5 ÷ 1000, then it can be easily done by shifting the decimal point to the left and the answer will be 8.9345

☛ Related Topics

• Adding Decimals
• Subtracting Decimals
• Multiplying Decimals
• Addition and Subtraction of Decimals
• Comparing Decimals
• Decimal Place Value
• Relationship Between Fractions and Decimals
• Decimals and Fractions

What is Dividing Decimals?

Dividing decimals means dividing a decimal number by another decimal number, or dividing a whole number by a decimal number as the case may be. It involves the division in which decimal numbers are used. We know that a decimal number is a number that consists of a whole number part and a fractional part which is separated by a dot which is known as the decimal point. For example, 56.34. So, when we talk about dividing decimals, it may mean 32.16 ÷ 2.3, or, 56.8 ÷ 4, or 2387 ÷ 9.2, and so on.

How to Divide Decimals by 10, 100, 1000?

In order to divide decimals by 10, 100, or 1000 we need to use the following rules:

• When we divide a decimal number by 10, we should move the decimal point to the left by one place. For example, if we need to divide 12.87 ÷ 10, then it can be easily done by shifting the decimal point to the left and the answer will be 1.287
• When we divide a decimal number by 100, we should move the decimal point to the left by two places. For example, if we need to divide 753.8 ÷ 100, then it can be easily done by shifting the decimal point to the left and the answer will be 7.538
• When we divide a decimal number by 1000, we should move the decimal point to the left by three places. For example, if we need to divide 432.7 ÷ 1000, then it can be easily done by shifting the decimal point to the left and the answer will be 0.4327

How to do Long Division with Decimals?

The long division in decimals is done in the same way as the regular long division of whole numbers. We just need to check if the divisor is a whole number or a decimal number.

• If the divisor is a whole number and the dividend is a decimal number we can divide in the usual way and keep the decimal point in the quotient according to the dividend. In other words, while dividing when we come across the decimal point in the dividend, we place a decimal point in the quotient at that particular step and continue dividing.
• If the divisor is a decimal number, we need to convert it to a whole number by shifting the decimal to the right until it becomes a whole number. Then, it is important to shift the decimal of the dividend with the same number of places. This can be done by multiplying the divisor by the powers of 10 and then accordingly multiplying the dividend also by the same power of 10. For example, if we need to divide 54.79 ÷ 1.5, we will multiply the divisor by 10 to remove the decimal point. this will be 1.5 × 10 = 15. Now, we need to multiply the dividend with the same number 10, so we get, 54.79 × 10 = 547.9. After this step, we can divide 547.9 ÷ 15 in the usual way and we get 36.52 as the quotient.

How to Divide Decimals by Decimals?

When we need to divide a decimal by a decimal, we need to convert the divisor to a whole number and then do the usual division. We convert the divisor to a whole number by shifting the decimal to the right until it becomes a whole number. This can be done by multiplying the divisor by the powers of 10 and then accordingly multiplying the dividend also by the same power of 10. For example, if we need to divide 78.91 ÷ 3.7, we will multiply the divisor by 10 to remove the decimal point. This will be 3.7 × 10 = 37. Now, we need to multiply the dividend with 10, so we get, 78.91 × 10 = 789.1. After this step, we can divide 789.1 ÷ 37 using long division and we get the quotient as 21.32

How to 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.

How to Divide Decimals by 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 as the quotient.

Can a Decimal be a Whole Number?

No, 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, and 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 decimal point of the divisor by multiplying it with a power of 10. Then, the dividend is also treated in the same way and multiplied by the same power of 10. Let us understand this with an example. For, example, to divide 12.5 ÷ 0.5, we need to multiply the divisor 0.5 by 10 so that it becomes a whole number. This will make it 0.5 × 10 = 5. Then, we will multiply the dividend also by 10 to get 12.5 × 10 = 125. After this step, we can divide 125 ÷ 5 = 25.

What is the Difference Between Multiplying and Dividing Decimals?

While multiplying decimals, we add the number of decimal places of the multiplicand and the multiplier and then place the decimal point in the product according to those number of places. For example: 0.0020 × 0.005 = 0.0000100. In this case, 0.0020 has 4 numbers after the decimal and 0.005 has 3 numbers after the decimal. This gives us 3 + 4 = 7. So, we will multiply the numbers normally and place the decimal point in the product after 7 places from the right. In division, we subtract the number of decimal places of the dividend and the divisor. For example, 0.0020 ÷ 0.005 = 0.4. In this case, 4 - 3 = 1, so we will divide the numbers normally (ignoring the decimals) and then place the decimal point after 1 place from the right.