Division of Decimal Numbers: A decimal number is one that has a decimal point between the whole number and the fractional part.

For example, let us say you are going to buy chocolate ice cream. The vendor tells you that the price of ice cream is ₹\(20\) and \(50\) paise. Now, if you want to express this whole amount in one figure, you will say that the price of the chocolate ice cream is ₹\(20.50.\) There are many such real-life situations in which you might be using decimals without even realizing it.

This article will discuss the division of decimal numbers by whole numbers, by other decimal numbers and by \(10,100,\;1000.\)… and so on.

Decimal Numbers

Every decimal number has two parts: The whole number part and the decimal (fractional) part.

So, in short, decimal numbers are defined as numbers with a decimal point followed by digits that show the fractional part. The number of digits in the decimal part determines the number of decimal places.

For example, the number of decimal places in \(2.4\) is \(1,\) in \(3.24\) is \(2\) and in \(0.0009\) is \(4.\)

The representation of the decimal number is shown below.

Division of Decimals

In a division, the three parts are defined as follows:

Before we start learning, let us first look at the key points.

1. When the divisor is less than \(1,\) the quotient is larger than the dividend.
2. When the divisor is greater than \(1,\) the quotient is smaller than the dividend.
3. The divisor cannot be \(0.\)

Check also

Division of Integers

Division of Fractions

Division of a Decimal Number by a Natural Number

Divide ordinarily, and in the quotient obtained, place the decimal just after dividing an integral part of the given decimal number.

Let us understand this with the help of an example.

Divide \(7.68\) by \(3\)

1. Divide the ones by \(3.\)

2. Mark the decimal point in the quotient directly above the decimal point in the dividend. Now, divide the tenths by \(3.\)

Learn About Decimal Number System

3. Align the same place values correctly. Finally, divide the hundredths by \(3.\)

4. If the remainder is \(0,\) we can multiply the quotient by the divisor and see if we get the dividend. \(2.56 \times 3 = 7.68\)

So, \(7.68 \div 3 = 2.56.\)

In the above example, we saw that dividing a decimal by a whole number works similarly to dividing by natural numbers.

Division of a Decimal Number by a Decimal Number

The following steps are to be followed while dividing a decimal number by a decimal number.

1. Form a fraction with the decimal number to be divided or the dividend as the numerator and the divisor decimal number as the denominator.
2. Multiply both the terms of the fraction formed in the previous step by \(10\) or \(100\) or \(1000,\) so that the decimal point in the denominator is removed, thus dividing the numbers.

Let us solve one example to understand the concept a little better.

Divide \(5.944\) by \(0.8.\)

\(5.944 \div 0.8 = \left( {5.944 \times 10} \right) \div \left( {0.8 \times 10} \right)\)

Move the decimal point \(1\) place to the right in both the dividend and the divisor by multiplying each by \(10.\)

Now, since the divisor is converted into a whole number, proceed with the division as done in the previous example.

Hence, \(5.944 \div 0.8 = 7.43\)

Thus while dividing decimals, if the divisor is not a whole number, then first move the decimal point in the divisor by a number of places until the divisor becomes a whole number. Then move the decimal point in the dividend by the same number of places. Then proceed to do the division and lastly put the decimal point in the quotient directly above the decimal point in the dividend.

Division by 10, 100 and 1000

What is the result of \(500\) times \(\frac{1}{{10}},\;\frac{1}{{100}}\) and \(\frac{1}{{1000}}\) ?

Confused??? Don’t be…..

\(500 \times \frac{1}{{10}} = \frac{{500}}{{10}} = 50\)
\(500 \times \frac{1}{{100}} = \frac{{500}}{{100}} = 5\)
\(500 \times \frac{1}{{1000}} = \frac{{500}}{{1000}} = 0.5\)

Now, let us represent \(500\) and the above results in a place value chart.

What do you notice about the place value of the digit \(5\) as we divide by \(10, 100\) and \(1000,\) respectively?

Now, closely observe the decimal point in each of the following.

When a number is divided by \(10,\) we move the decimal point \(1\) place to the left.
For example,

When a number is divided by \(100,\) we move the decimal point \(2\) places to the left.
For example,

When a number is divided by \(1000,\) we move the decimal point \(3\) places to the left.
For example,

When there is no digit in the one’s place, we write \(0\) as a placeholder. Thus, \(765\) is written as \(0.765.\)

Similarly, according to the number of zeros in the multiples of \(10,\) the decimal points will be shifted to the left while dividing a number by multiples of \(10.\)

Solved Examples – Division of Decimal Numbers

Q.1. Divide \(5.15\) by \(5.\)
Ans: Divide ordinarily, and in the quotient obtained, place the decimal just after dividing an integral part of the given decimal number.
Therefore, \(\frac{{5.15}}{5} = 1.03\)

Q.2. Divide \(13.797\) by \(0.21.\)
Ans: Given: \(\frac{{13.797}}{{0.21}}\)
First, make the divisor \(0.21\) a whole number. Hence, \(0.21 \times 100 = 21.\) Multiply both the dividend and divisor by \(100.\)
\(\frac{{13.797 \times 100}}{{0.21 \times 100}} = \frac{{1379.7}}{{21}}\)
Thus, by multiplying both the divisor and the dividend by \(100,\) we eliminate the decimal point in the divisor.

Thus, \(13.797 \div 0.21 = 65.7\)

Q.3. Divide the given decimal numbers.
a) \(\frac{{5.065}}{{0.05}}\) b) \(\frac{{36.8}}{{1.6}}\)
Ans: Form a fraction with the decimal number to be divided as the numerator and the other decimal number as the denominator. Multiply both the terms of the fraction formed in the previous step by \(10\) or \(100\) or \(1000,\) so that the decimal point in the denominator is removed, and thus, divide the numbers.
a) \(\frac{{5.065}}{{0.05}}\)
\(\frac{{5.065}}{{0.05}} = \frac{{5.065 \times 100}}{{0.05 \times 100}} = \frac{{506.5}}{5} = 101.3\)
b) \(\frac{{36.8}}{{1.6}} = \frac{{36.8 \times 10}}{{1.6}} = \frac{{368}}{{16}} = 23\)

Q.4. A \(6.2\,{\rm{m}}\) long pipe weighs \(7.44\,{\rm{kg}}{\rm{.}}\) How much does \(1\,{\rm{m}}\) long pipe weigh?
Ans: Since \(6.2\,{\rm{m}}\) long pipe weighs \(7.44\,{\rm{kg}},\,1\,{\rm{m}}\) long pipe weighs \(\frac{{7.44}}{{6.2}}\;{\rm{kg}}.\)
Now, multiply both the divisor and the dividend by \(10\) to make the divisor \(6.2\) a whole number.
\(\frac{{7.44}}{{6.2}} = \frac{{7.44 \times 10}}{{6.2 \times 10}} = \frac{{74.4}}{{62}}\)
Therefore, \(\frac{{74.4}}{{62}} = 1.2\)
Hence, \(1\,{\rm{m}}\) long pipe weighs \(1.2\,{\rm{kg}}{\rm{.}}\)

Q.5. Divide and find the quotient without actual division.
a) \(8.34 \div 10\) b) \(8.34 \div 100\) c) \(8.34 \div 1000\)
Ans: a) \(8.34 \div 10.\)
We can see that there is only one zero after \(1\) in the divisor, so shift the decimal point to the left by \(1\) place.
Hence, \(8.34 \div 10 = 0.834.\)
b) \(8.34 \div 100.\)
Again, there are two zeros after \(1\) in the divisor, shifting the decimal point to the left by \(2\) places.
Hence, \(8.34 \div 100 = 0.0834.\)
c) \(8.34 \div 1000.\)
There are three zeros after \(1\) in the divisor, shifting the decimal point to the left by \(3\) places.
Hence, \(8.34 \div 1000 = 0.00834.\)

Summary

In this article, we had a quick discussion about decimal numbers. Then we learned the various methods to divide the decimal numbers by natural numbers, decimal numbers by decimal numbers, and decimal numbers by \(10, 100\) or \(1000.\) In addition to this, we also learned the long division method of diving the decimal numbers. We also learned the long division methods to divide.

Learn About the Methods of Division

FAQs on Division of Decimal Numbers

Q.1. How do you divide a number by a decimal number?
Ans: Following steps are to be followed while dividing a number by a decimal number:
a) Form a fraction with the number to be divided as the numerator and the decimal number as the denominator.
b) Multiply both the terms of the fraction formed in the previous step by \(10, 100\) or \(1000\) so that the decimal point in the denominator is removed, thus dividing the numbers.

Q.2. How do you divide decimals by long division?
Ans: Divide in an ordinary way, and in the quotient obtained, place the decimal just after the division of an integral part of the given decimal number. To be more precise, the following steps explain the whole process of the long division process.
a) Firstly, write down the division in the standard form. Start by dividing the whole number part by the divisor.
b) Next, place the decimal point in the quotient above the decimal point of the dividend. And, then, bring down the tenth digit.
c) Lastly, divide and bring down the next digit. Divide until \(0\) is obtained in the remainder. Thus, the decimal in the quotient is similar or equal to the decimal in the dividend.

Q.3.  How do you divide a decimal by \(10, 100\) and \(1000\)?
Ans: When a number is divided by \(10,\) we move the decimal point \(1\) places to the left.
When a number is divided by \(100,\) we move the decimal point \(2\) places to the left.
When a number is divided by \(1000,\) we move the decimal point \(3\) places to the left.
For example, \(\frac{{134.32}}{{10}} = 13.432,\,\frac{{134.32}}{{100}} = 1.3432\) and \(\frac{{134.32}}{{10}} = 13.432,\,\frac{{134.32}}{{1000}} = 1.3432.\)

Q.4. What are decimal numbers?
Ans: We can define decimal numbers as a number with a decimal point followed by digits that show the fractional part. The number of digits in the decimal part determines the number of decimal places.

Q.5. What should be done first in dividing decimal?
Ans: The first thing to be done in dividing is to move the decimal point to the right to make the decimal number to the whole number by multiplying by \(10, 100, 1000\) and so on and then move the dividend’s decimal point to the same number of places to the right.

Now you are provided with all the necessary information on the division of decimal numbers and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.