Educational

Decimal Expansion of Rational Numbers The Decimal Expansion of a Rational Number Fill in the Blank: The decimal expansion of a rational number is either terminating or non-terminating repeating. Explanation: Terminating decimal: Ends after a finite number of digits (e.g., \(0.5\)) Non-terminating repeating decimal: Continues forever but repeats (e.g., \(0.\overline{3}\)) Final Answer: Terminating, Non-terminating repeating

Visualise 5.3̅7 on Number Line Visualise \(5.3\overline{7}\) on the Number Line upto 5 Decimal Places Diagram (Successive Magnification) 5 6 5.3 5.3 5.4 5.37 5.37 5.38 5.377 5.377 5.378 5.3777 Construction Method: Step 1: Mark 5 and 6 on the number line. \[ 5 < 5.3777 < 6 \] Step 2: Divide [5, 6] into

Representation of √3.5, √9.4, √10.5 on Number Line Represent \( \sqrt{3.5}, \sqrt{9.4}, \sqrt{10.5} \) on the Number Line Construction Method: Step 1: Draw a number line and mark O (0) and A such that OA = 3.5 units. Step 2: At point A, draw a perpendicular AB of length 1 unit. Step 3: Join OB.

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