May 2026

Visualise 2.665 on Number Line Visualise \(2.665\) on the Number Line Using Successive Magnification Diagram (Successive Magnification) 2 3 2.6 2.6 2.7 2.66 2.66 2.67 2.665 Construction Method: Step 1: Mark 2 and 3 on the number line. \[ 2 < 2.665 < 3 \] Step 2: Divide the interval [2, 3] into 10 equal […]

Representation of √6, √7, √8 on Number Line Represent \( \sqrt{6}, \sqrt{7}, \sqrt{8} \) on the Number Line Construction Method: To Construct \( \sqrt{6} \): Draw a number line and mark O (0) and A such that OA = 5 units. At point A, draw a perpendicular AB of length 1 unit. Join OB. \[

Complete the Sentences – Real Numbers Complete the Following Sentences Solution: (i) Every point on the number line corresponds to a real number which may be either rational or irrational. (ii) The decimal form of an irrational number is neither terminating nor repeating. (iii) The decimal representation of a rational number is either terminating or

Examples of Irrational Numbers Operations Examples of Irrational Numbers Based on Operations Solution: (i) Difference is a Rational Number \[ \sqrt{2} – \sqrt{2} = 0 \ (\text{rational}) \] (ii) Difference is an Irrational Number \[ \sqrt{5} – \sqrt{3} \] This is irrational. (iii) Sum is a Rational Number \[ (2 + \sqrt{3}) + (2 –

True or False – Rational and Irrational Numbers Find Whether the Following Statements are True or False Solution: (i) Every real number is either rational or irrational. All real numbers can be classified into two categories: rational and irrational. Answer: True (ii) \( \sqrt{2} \) is an irrational number. \( \sqrt{2} \) cannot be expressed

Irrational Numbers Between 0.1 and 0.12 Find Two Irrational Numbers Between 0.1 and 0.12 Solution (Direct Method): \[ 0.1 < x < 0.12 \] Choose non-terminating, non-repeating decimals between them: \[ 0.1010010001…, \quad 0.11010010001… \] These numbers lie between 0.1 and 0.12 and are non-terminating and non-repeating, hence irrational. Final Answer: \[ 0.1010010001…, \quad 0.11010010001…

Irrational Numbers Between 0.5 and 0.55 Find Two Irrational Numbers Between 0.5 and 0.55 Solution (Direct Method): \[ 0.5 < x < 0.55 \] Choose non-terminating, non-repeating decimals between them: \[ 0.510100100010000…, \quad 0.520200200020000… \] These numbers lie between 0.5 and 0.55 and are non-terminating, non-repeating. Final Answer: \[ 0.510100100010000…, \quad 0.520200200020000… \] Next Question

Irrational Numbers Between 5/7 and 9/11 Find Three Irrational Numbers Between \( \frac{5}{7} \) and \( \frac{9}{11} \) Solution (Direct Method): \[ \frac{5}{7} = 0.714285… \quad \text{and} \quad \frac{9}{11} = 0.818181… \] So, \[ 0.714… < x < 0.818... \] Choose non-terminating, non-repeating decimals between them: \[ 0.721001000100001…, \quad 0.752002000200002…, \quad 0.801003000300003… \] All these

Rational and Irrational Numbers Between Given Decimals Find a Rational and an Irrational Number Between Given Decimals Question: Find a rational number and also an irrational number lying between \(0.3030030003…\) and \(0.3010010001…\). Solution: First arrange the numbers: \[ 0.3010010001… < 0.3030030003... \] Step 1: Rational Number Choose a terminating decimal between them: \[ 0.302 \]

Irrational Number Between Given Decimals Find an Irrational Number Between Given Decimals Question: Find one irrational number between \(0.2101\) and \(0.\overline{2}\) (i.e., \(0.222…\)). Concept Used: An irrational number is a non-terminating, non-repeating decimal. :contentReference[oaicite:0]{index=0} Solution: We are given: \[ 0.2101 < \ ? \ < 0.2222... \] We need a number between these which is