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Division Of Decimals

Division of Decimals by Whole Numbers

Dividing decimals by whole numbers is almost same as dividing whole numbers.

Division of decimals by whole numbers can be done by the following steps:

Step 1: Ignore the decimal point.

Step 2: Use long division method to find quotient.

Step 3: Count the digits of the dividend after the decimal point.

Step 4: The number of digits after the decimal point in quotient should be same as the number of digits after the decimal point in dividend.

For example: \(9.1÷7\)

Step 1: Ignore the decimal point. 

\(91÷7\)

Step 2: Using long division method.

Here, the dividend has one digit after the decimal point.

\(9.\color{red}1\rightarrow \text {One digit}\)

Thus, the quotient will also have one digit after the decimal point.

Quotient \(13\rightarrow1.3\)

Hence, \(1.3\) is the quotient of \(9.1\) by \(7\)

Note : When we divide decimals by power of \(10\), then we can simply move the decimal point to the left, by the number of places per multiple of \(10\).

 

 

Example 1 : \(17.25\div1000\)

Here, we will move decimal point by three place values.

Example 2 : \(57.6\div10\)

Here, we will move decimal point by one place value.

Illustration Questions

Evaluate \(3.45÷15\)

A \(.25\)

B \(.23\)

C \(2.3\)

D \(2.5\)

×

Given: \(3.45÷15\)

Ignore the decimal point.

\(345÷15\)

Use long division method.

 

image

The dividend has two digits after the decimal point.

\(3.\color{red} {45}\rightarrow \text {2 digits}\)

So, the quotient will also have two digits after the decimal point.

Quotient \(23\rightarrow.23\)

Thus, \(.23\) is the final answer.

Hence, option (B) is correct.

Evaluate \(3.45÷15\)

A

\(.25\)

.

B

\(.23\)

C

\(2.3\)

D

\(2.5\)

Option B is Correct

Division of Decimals up to Tenths Place

Dividing decimals by other decimals is almost same as dividing whole numbers.

Division of two decimal numbers can be done by the following steps:

Step 1: Make the divisor into a whole number by multiplying it by a power of ten.

Step 2: Since, we multiply the divisor by a power of \(10\), thus we also have to multiply the dividend by the same power of ten.

Step 3: Now, divide as a whole number.

For example: Dividing \(10.8\) by \(4.5\)

First, multiply the divisor by \(10\) to make it into a whole number.

\(4.5×10=45\)

Also, multiply the dividend by the same power of ten.

\(10.8×10=108\)

Now, divide \(108\) by \(45\) (both whole numbers).

We find that it is not possible to divide \(18\) by \(45\).

So, we put the decimal point after \(2\) in the quotient and then place a zero to the end of \(18\), making it \(180\).

Hence, \(2.4\) is the quotient of \(10.8÷4.5\)

 

Hence, \(2.4\) is the quotient of \(10.8÷4.5\)

 

Illustration Questions

Evaluate \(8.5÷2.5\)

A \(6.0\)

B \(4.5\)

C \(11.0\)

D \(3.4\)

×

First, multiply the divisor by \(10\) to make it into a whole number;

\(2.5×10=25\)

Now, we also multiply the dividend by the same power of \(10\);

\(8.5×10=85\)

Now, divide \(85\) by \(25\) (both whole numbers) 

 

image

Now, it is not possible to divide \(10\) by \(25\).

So, we put the decimal point after \(3\) in the quotient and then place a zero to the end of \(10\), making it \(100\).

image

Thus, \(3.4\) is the quotient of \(8.5÷2.5\) 

Hence, option (D) is correct.

Evaluate \(8.5÷2.5\)

A

\(6.0\)

.

B

\(4.5\)

C

\(11.0\)

D

\(3.4\)

Option D is Correct

Division of Decimals up to Hundredths Place

Dividing decimals by other decimals is almost same as dividing whole numbers.

Division of two decimal numbers can be done by the following steps:

Step 1: Make the divisor into a whole number by multiplying it by a power of ten.

Step 2: Since, we multiply the divisor by a power of \(10\), thus we also have to multiply the dividend by the same power of ten.

Step 3: Now, divide as a whole number.

For example: Dividing \(4.55\) by \(0.13\)

First, multiply the divisor by \(100\) to make it into a whole number.

\(0.13×100=13\)

Now, we also multiply the dividend by the same power of ten.

\(4.55×100=455\)

Now, divide \(455\) by \(13\) (both whole numbers).

Hence, \(35\) is the quotient of \(4.55÷0.13\)

 

Illustration Questions

Evaluate​ \(1.26÷0.09\)

A \(14\)

B \(1.35\)

C \(0.14\)

D \(1.035\)

×

First, multiply the divisor by \(100\) to make it into a whole number.

\(0.09×100=9\)

 

Now, we also multiply the dividend by the same power of ten.

\(1.26×100=126\)

Now, divide \(126\) by \(9\) (both whole numbers).

image

Thus, \(14\) is the quotient of \(1.26÷0.09\)

Hence, option (A) is correct.

Evaluate​ \(1.26÷0.09\)

A

\(14\)

.

B

\(1.35\)

C

\(0.14\)

D

\(1.035\)

Option A is Correct

Miscellaneous

Division of decimal numbers with different place values can be done by following these steps:

Step 1: Make the divisor into a whole number by multiplying it by a power of ten.

Step 2: Since, we multiply the divisor by a power of \(10\), thus we also have to multiply the dividend by the same power of ten.

Step 3: Ignore the decimal point.

Step 4: Use long division method.

For example: Divide \(0.624\) by \(0.6\)

  • First, multiply the divisor by \(10\) to make it into a whole number.

           \(0.6×10=6\)

  • Now, we also multiply the dividend by the same power of ten.

           \(0.624×10=6.24\)

  • Ignore the decimal point 

\(624÷6\)

  • Using long division method

As the dividend has two digits after the decimal point.

\(6.\color{red}{24}\rightarrow2\text { digits}\)

So, the quotient will also have two digits after the decimal point.

Quotient \(104\rightarrow 1.04\)

Hence, \(1.04\) is the quotient of \(0.624÷0.6\)

Illustration Questions

Evaluate 

A \(0.4\)

B \(0.0004\)

C \(40\)

D \(400\)

×

Given: \(0.16÷0.004\)

First, multiply the divisor by \(1000\) to make it into a whole number.

\(0.004×1000=4\)

Now, we also multiply the dividend by the same power of ten.

\(0.16×1000=160\)

Now, divide \(160\) by \(4\) (both whole numbers).

image

Thus, \(40\) is the quotient of \(0.16÷0.004\)

Hence, option (C) is correct.

Evaluate 

image
A

\(0.4\)

.

B

\(0.0004\)

C

\(40\)

D

\(400\)

Option C is Correct

Dividing Decimals Using Area Model

To divide means to split into equal parts.

For example: Divide \(2.6\) by \(1.3\)

Here, we will find how many times of \(1.3\) makes \(2.6\)

To find \(1.3\) in \(2.6\), mark \(1.3\) in the shaded part.

There are two \(1.3\)'s in \(2.6\)

Hence, \(2.6\,\div\,1.3=2\)

 

We can also divide decimal numbers by whole numbers using area model.

For example: Divide \(2.46\) by \(3\)

Now, we divide \(2.46\) equally into \(3\) groups.

Each group contains \(82\) shaded squares.

Hence, \(2.46\,\div\,3=0.82\)

Illustration Questions

Which one of the following models represents quotient of \(3.69\,\div\,3\)?

A

B

C

D

×

To find the quotient of \(3.69\) by \(3\), we will divide \(3.69\) equally into 3 groups.

image

Each group contains \(123\) shaded squares.

Thus, 

image

Hence, option (A) is correct.

Which one of the following models represents quotient of \(3.69\,\div\,3\)?

A image
B image
C image
D image

Option A is Correct

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