Question

difference between rational and irrational number.explain ​

Answer 1

$\huge{\boxed{\sf{ANSWER-}}}$

$\huge{\boxed{\sf{RATIONAL\:NUMBERS:}}}$

=) ANY NUMBER THAT CAN BE REPRESENTED IN THE FORM $\frac{p}{q}$, WHERE p,q € Z, SUCH THAT p AND q ARE CO-PRIME, AND q NOT=0(BECAUSE DIVISION BY ZERO IS INVALID.✔✔

=)WHEN q not=1 AND p, q HAVE NO COMMON FACTOR EXCEPT 1,(WHERE p AND q ARE BOTH POSITIVE) THE RATIONAL NUMBERS ARE CALLED FRACTIONS.✔✔

=) RATIONAL NUMBERS WHEN REPRESENTED IN DECIMAL FORM ARE EITHER 'TERMINATING'OR 'NON- TERMINATING BUT RECURRING'.✔✔

E.g.,$\frac{5}{4}=1.25\:\:(terminating\:in zeros)\\\frac{5}{3}=1.666....(non\:terminating\:but\:recurring)$

$\huge{\boxed{\sf{IRRATIONAL\:NUMBERS-}}}$

=) NUMBERS WHICH CANNOT REPRESENTED IN $\frac{p}{q}$ FORM(WHERE p, q € Z AND q not=0)ARE CALLED IRRATIONAL NUMBERS.✔✔

=) IN DECIMAL REPRESENTED, THEY ARE NEITHER TERMINATING NOR RECURRING HENCE, ALL SURDS FALL IN THIS CATEGORY.✔✔

E.g.,$\sqrt{2},{15}^{\frac{1}{3}},\pi$

Answer 2

Rational Numbers- A number that can be expressed as a ratio of two number (p/q form) are termed as Rational Number.

Irrational Numbers- A numbers that cannot be expressed as a ratio of two numbers are termed as Irrational Number.