5th Class Mathematics Operation of Decimals Decimals and Its Operations

 

Decimals and Its Operations

 

Decimals

A fraction with the denominator as power of 10 (like 10,100, 1000 etc.) is called decimal. It is expressed as the numbers with a point in between, called decimal point. In other words, decimal consists of two parts which are separated by a decimal point.

 

• Example:

2.564, 0.0023, 3.2565, 5431.23 are decimals.

 

Expanded Form of Decimals

Expanded form of a decimal represents the addition of place values of the digits, respective to their positions in the decimal.

 

• Example:

Write the expanded form of the decimal 69.4756.

 

Solution: \[60+9+\frac{4}{10}+\frac{7}{100}+\frac{5}{1000}+\frac{6}{10000}\]

 

• Example:

Write the decimal 0.99 in expanded form.

 

Solution: \[\frac{9}{10}+\frac{9}{100}\]

 

Decimal Places

The number of digits placed in right to the point of a decimal is called the decimal places of that decimal.

 

• Example: The decimal 564.3549 has four decimal places because it has four digits right to the point.

 

Like Decimals

Like Decimals have same number of decimal places.

 

• Example:

45.32965 and 0.00236 are like decimals, because they have the same number of decimal places.

 

Unlike Decimals

Unlike decimals have different number of decimal places.

 

• Example:236 and 236.23 are unlike decimals, because they have different number of decimal places.

 

Equivalent Decimals

The decimals which have same value are called equivalent decimals.

 

• Example:52 and 4.5200 are equivalent decimals, because they have same value.

 

Comparison of Decimal

Step 1: Compare the integral parts of the decimals, the decimal having greater Integral part is greater.

Step 2: If the integral parts are equal, compare the decimal part. The decimal having greater decimal part is greater.

 

• Example:

Compare between 542.565 and 502.9349 and find which is greater.

Solution: 542.565 is greater than 502.9349 because 542.565 has greater integral part

 

• Example:

Compare between 878.0213 and 878.1213 and find which is greater?

Solution: 878.1213 is greater than 878.0213 because 878.1213 has greater decimal par.

 

Operation on Decimals

Operation on decimals means how to add two or more than two decimals, how to subtract a decimal from other decimal, how to multiply decimals, and how to divide a decimal by other decimal.

 

Addition of the Decimals

Step1: Convert the addends into like decimals.

Step 2: Arrange the addends one below other in columns so that decimal points come in the same column.

Step 3: Now add the digits which are in the same column, write the sum directly in the below column and place a point in the point column.

 

• Example:

Add 745.547 and 0.21402

 

Solution:\[\begin{align}

  & \underline{\begin{align}

  & \,\,\,745.54700 \\

 & +\,\,\,\,\,\,0.21402 \\

\end{align}} \\

 & \,\,\,745.76102 \\

\end{align}\]

Therefore, the answer is 745.76102.

 

Subtraction of Decimals

Step 1: Convert the minuend and subtrahend into like decimals.

Step 2: Arrange the digits of minuend and subtrahend column wise, one below other, so that decimal points come in the same column.

Seep 3:  Now subtract the digits column wise from right to left. Write the difference directly below the respective digits and place a point in the point column.

 

• Example:

  Subtract 347.6544 from 348.5.

    

 

Therefore, answer is 0.8456

Multiplication of Decimals by Power of 10

Step1: Shift the point in the decimal to right as many places as there are zeroes the power of 10 contains.

Step 2:  If there are short of digits to the right of the point in the decimal, add zeroes right to it and follow the first step.

 

• Example:

Find the product of 5487.476 and 1000.

Solution: \[5487.476\times 1000=5487476\]

 

Multiplication of a Decimal by Another Decimal

Step1:   Remove the point from the decimals and multiply them like whole numbers.

Step2:  Insert a point in the product so that number of decimal places of the product is equal to the sum of the number of decimals places of the multiplier and the multiplicand.

 

• Example:

Multiply 56.45 and 2.03.

Solution: \[56.45\times 2.03=114.5935\]

 

Division of a Decimals

step1: Convert the decimals into fractions.

step2: Divide the fraction by divisor fraction.

 

• Example: Divide 16.47 by 3.66.

Solution:\[16.47\div 3.66\text{ }=\frac{1647}{100}\div \frac{366}{100}=\frac{1647}{366}=4.5\]

 

Division of a Decimal by the Power of 10

step1:   Shift the point in the decimal to left as many places as there are zeroes the power of 10 contains.

step2: If there are short of digits left to the point in the decimal, add zeroes left to it and follow the step 1.

• Example: Divide 2345.63 by 1000.

Solution:\[2345.63\div 1000=2.34563\]