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DECIMALS
    Numbers of the form 12.4, 362.49, 148.3672 etc. are said to be in decimal form.

A decimal number can be expressed into two parts
1.    The whole number
2.    The decimal part in a decimal number. 
       The parts are seperated by a point (.) called the decimal point.
       In a decimal number the number on left hand side of the decimal is called the whole number part and the number on the right hand side of the point is called the decimal part.
       For example, In the number 13.436, 13 is the whole number part and 436 is the decimal part.

      Decimal Places - The number of digits in the decimal part give the number of decimal places.
      For example, 140.034 has 3 decimal places

      Like Decimals - Decimal numbers having same number of decimal places are called like fractions.
      For example, 12.32, 143.93, 160.04 etc. are like decimals having two decimals places each.

     Unlike Decimals - Decimal numbers having different number of decimal places are called unlike decimals.
     For example, 1.362, 3.43, 16.1 etc.
     Note: Placing any number of zeroes at the extreme right of the last digit of the decimal place does not change its value. Thus 44.083 = 44.08300 = 44.083000 etc.


Comparison of Decimals numbers
    Steps for comparison of decimal numbers :
    (i)     Convert the decimal number into like decimals by placing zeroes to the right of the decimal.
    (ii)     Compare the whole number part. The number with greater whole number part is greater.
    (iii)     If the whole number parts are equal, compare the first digit after decimal. The number with the larger digit in the place right to decimal will be greater.
    (iv)     If the digit to the right of the decimal is equal then compare the 2nd digit from the right of decimal then the 3rd digit to the right of decimal and so on.

Illustration 
        Write the following decimal number in ascending order: 6.3, 5.3, 6.03, 4.308, 5.45  

Solution
        Convert the given fractions into like fraction.
        6.300, 5.300, 6.030, 4.308, 5.450 arranging in ascending order after comparison of digits we get,
            4.308 < 5.300 < 5.450 < 6.030 < 6.300

Conversion of decimal number into fraction 
    In order to convert a decimal number into fraction, the digits of the decimal number are kept as numerator without the decimal, and the denominator is kept as 1 followed by the same number of zeroes as there were digits after decimal.

Operation of Decimals 
    Addition and Subtraction of Decimal Numbers
    Steps to add or subtract decimal numbers:
    (i)    Convert all the decimal number into like decimals 
    (ii)    Add or subtract as required, as per rules of addition or subtraction of whole numbers.
    (iii)    Place the decimal under decimal point in the given numbers.


Illustration 1
        Add : 13.46, 219.54, 2.084
    Solution  

               


Illustration 2
        Subtract :  148.23 – 30.018
   Solution    
             

 

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