What is Decimal Numbers? Terminating and Non-terminating | Recurring and Non-recurring decimal

Decimal Number

Decimal numbers are numbers that are written according to their place value. The decimal point is used to separate whole part from number value less than one.A symbol is used " . ", this is called decimal point.

Example: 65.894 where 65 is a whole part and 894 is a fractional part.

Type of Decimals

1. Terminating Decimals 

2. Non-terminating Decimals

1. Terminating Decimals

Every fraction a/b can be expressed as a decimal. If the decimal expression of a/b terminates i.e. comes to end, then the decimal so obtained is called a terminating decimal.

Example: 1/2 = 0.5 

                 5/4 = 1.25

                13/5= 2.6

Thus, each of the numbers 1/2, 5/4 and 13/5 can be expressed in the form of a terminating decimal.

2. Non-terminating Decimals

While expressing a fraction in the form of decimal, when we perform division we get some remainder. If the division process does not end i.e. remainder is not equal to zero, then such decimal is known as non-terminating decimal. 

Example: 5/3 = 1.666666....... = 1.6

              16/45 = 0.355555 ...... = 0.35

                 

These are non-terminating Decimals

Type of Non-terminating Decimals

1. Recurring Decimal

2. Non-recurring Decimal

We can understand above these terms with some examples.