**3.14159 **is rational or irrational, is an important irrational number called PI is denoted by **mathematical symbol π ** Which denote the constant ratio of the circumstance of any circle to the length of the diameter

### FORMULA OF Pi (π)

=

An approximate value of is 22/7, a better approximation is 355/113

and a still better approximation is 3.14159.correct to 5 lac decimal places

has been determined with the help of the computer

hence, 3.14159 is rational or irrational prove upper discussion.

#### 0.5 is rational number

**Yes, 0.5 = 1/2 is a rational number by rational number definition**. Which number can be written in the form p/q where, p is an any number, q is also an any number and q ≠ 0

**mathematical definition of rational number**

**p, q ∈ Z (set of integer) and (∧) q ≠ 0**

The numbers √16, 3.7, 4 are the example of rational number.

√16 can be reduced to the form **p/q where p, q ∈ Z** and q does not equal to zero (q≠0)

because:

√16=4= 4/1

#### IRRATIONAL NUMBER

The number cannot be written in the form p/q

Where p, q ∈ Z and q ≠ 0

The numbers √2, √3, 7/√5, √5/16 are irrational numbers.

##### Non-terminating decimal:

A non-terminating, non-recurring decimal is a decimal

which is neither terminate nor it is recurring .it is nor possible

to convert such a decimal into common fraction.

Thus, a non-terminating , non-recurring decimal represent as an irrational number

**EXAMPLE OF IRRATIONAL NUMBER**

(1) 1.4042135……. is an irrational number.

(2) 1.719975987….. is an irrational number.

(3) 0.123455678……………. is an irrational number.

##### Terminating decimal:

A decimal, only a finite number which has only a finite number of digits

is called a** terminating decimal**.

**Example of terminating decimal :**

(1) 0 .17 (=17/100) is a rational number terminating.

0,4444 (=4444/1000) is a rational number terminating

**Recurring terminating decimal:**

another type of rational number recurring or periodic decimal is a decimal

in which one or more digit repeat definitely

##### Example of recurring terminating decimal

(1) 0.124124124….. is recurring terminating decimal

(2) 4.14561456…… is recurring terminating decimal.

RELATED POST