Question

Make a detailed chart of NUMBER SYSTEM giving special emphasis on the Rational and Irrational numbers with at least 5 examples on each , their definition , properties etc​

Answer 1

Answer :-

Rational Numbers :-

• A real number which can be written in the form of p/q where q ≠ 0 .

5 Examples :-

• 0 = 0/1 => p = 0 => q = 1 here p is 0 but q ≠ 0 .
• 3/4 => p = 3 => q = 4 and q ≠ 0 .
• 5/8 => p = 5 => q = 8 and q ≠ 0 .
• √81 = ± 9 => (9/1) or (-9/1) . here q ≠ 0 .
• 22/7 => p = 22 => q = 7 and q ≠ 0 .

Irrational Numbers :-

• Real numbers which can not be written in the form of p/q where q ≠ 0 .

5 Examples :-

• √2 = 1.414213____
• π = 3.142857_____
• 1/0
• √(2/3)
• √10

Properties of Rational and Irrational numbers :-

• All whole numbers are rational numbers .
• All integers are rational numbers .
• Rational numbers are closed under addition, subtraction, and multiplication.
• Rational + Rational = Rational number .
• Rational - Rational = Rational number .
• Rational * Rational = Rational number .
• Rational number say p/q = (p * n)/(q * n) = p/q or, (p ÷ n) / (q ÷ n) = p/q . { Meaning is a rational number remains the same if we divide or multiply both the numerator and denominator with the same factor .}
• The square roots which are not perfect squares are irrational number.
• The decimal expansion of an irrational number is non terminating and non recurring .
• Irrational + Rational = Irrational number .
• Irrational * Irrational = Irrational / Rational number . { Irrational number examples :- √2 * √3 = √6 , Rational number Examples :- √2 * √2 = 2 , (√3 + 1)(√3 - 1) = 3 - 1 = 2 ,√2 * √32 = √64 = 8 . }
• Irrational + Irrational = Irrational / Rational number . { Ex. √2 + √3 = (√2 + √3) = Irrational number and , (4 + √3) + (-√3) = 4 = Rational Number .

Learn more :-

prove that √2-√5 is an irrational number

https://brainly.in/question/37780143

Answer 2

Answer:

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Step-by-step explanation:

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