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.
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