Number System

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A rational number is any number that can be expressed in the form p/q, where p and q are integers and q ≠ 0. Examples: 3/4, -2/5, 7 (which is 7/1), 0 (which is 0/1).

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Yes, zero is a rational number because it can be written in the form p/q where p = 0 and q is any non-zero integer. For example: 0 = 0/1 = 0/2 = 0/3, etc.

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False. Every whole number is NOT a natural number because zero is a whole number but not a natural number. Natural numbers = {1, 2, 3, 4, ...} while Whole numbers = {0, 1, 2, 3, 4, ...}…

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True. Every integer m can be expressed in the form m/1, which is in the form p/q where p = m, q = 1, and q ≠ 0. Therefore, every integer is a rational number.

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Method 1: Find the average (r + s)/2 of the two numbers r and s. Method 2: Convert both numbers to have the same denominator (n+1 where n is the number of rational numbers needed), then list numbers w…

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An irrational number is a real number that cannot be expressed in the form p/q where p and q are integers and q ≠ 0. These have non-terminating, non-recurring decimal expansions. Examples: √2, √3, π, …

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Construct a right triangle with legs of length 1 unit each. By Pythagoras theorem, hypotenuse = √(1² + 1²) = √2. Place one vertex at origin O, use compass with center O and radius equal to hypotenuse …

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No. The square roots of perfect squares are rational. For example: √4 = 2, √9 = 3, √16 = 4, √25 = 5, etc. However, square roots of non-perfect squares like √2, √3, √5, √7, etc. are irrational.