May 2026

Rational Numbers Between Given Decimals Find Two Rational Numbers Between Given Decimals Question: Give two rational numbers lying between \(0.515115111511115…\) and \(0.5353353335…\). Concept Used: Between any two real numbers, there are infinitely many rational numbers, so we can always choose convenient terminating decimals between them. :contentReference[oaicite:0]{index=0} Solution: First compare the numbers: \[ 0.515115111511115… < 0.5353353335... […]

Rational Numbers Between Two Decimals Find Two Rational Numbers Between Given Decimals Question: Give two rational numbers lying between \(0.232332333233332…\) and \(0.212112111211112…\). Concept Used: Between any two real numbers, there are infinitely many rational numbers. :contentReference[oaicite:0]{index=0} Solution: First, compare the given numbers: \[ 0.212112111211112… < 0.232332333233332... \] Now choose simple terminating decimals between them. We

Rational or Irrational from Equations Find Whether Variables Represent Rational or Irrational Numbers Question: In the following equations, find whether the variables represent rational or irrational numbers: (i) \( x^2 = 5 \) (ii) \( y^2 = 9 \) (iii) \( z^2 = 0.04 \) (iv) \( u^2 = \frac{17}{4} \) (v) \( v^2 =

Rational and Irrational Numbers with Decimal Representation Identify Rational or Irrational Numbers and Give Decimal Representation Question: Identify whether the following numbers are rational or irrational. Give decimal representation of rational numbers: (i) \( \sqrt{4} \) (ii) \( 3\sqrt{18} \) (iii) \( \sqrt{1.44} \) (iv) \( \sqrt{\frac{9}{27}} \) (v) \( -\sqrt{64} \) (vi) \( \sqrt{100}

Rational or Irrational Numbers Examine Whether the Following Numbers are Rational or Irrational Question: Examine whether the following numbers are rational or irrational: (i) \( \sqrt{7} \) (ii) \( \sqrt{4} \) (iii) \( 2 + \sqrt{3} \) Solution: (i) \( \sqrt{7} \) 7 is not a perfect square. Hence, \( \sqrt{7} \) cannot be expressed

Difference Between Rational and Irrational Numbers Explain How Irrational Numbers Differ from Rational Numbers Question: Explain how irrational numbers differ from rational numbers. Explanation: The difference between rational and irrational numbers is mainly based on whether the number can be written in the form \[ \frac{p}{q} \] where \(p\) and \(q\) are integers and \(q

Definition of Irrational Number Define an Irrational Number Question: Define an irrational number. Definition: An irrational number is a number that cannot be expressed in the form \[ \frac{p}{q} \] where \(p\) and \(q\) are integers and \(q \ne 0\). Its decimal expansion is non-terminating and non-repeating. Examples: \(\sqrt{2}\) \(\sqrt{3}\) \(\pi\) These numbers cannot be

Convert 0.6 + 0.7̅ + 0.47̅ into Fraction (p/q) Express \(0.6 + 0.\overline{7} + 0.4\overline{7}\) in the Form \( \frac{p}{q} \) Question: Express \(0.6 + 0.\overline{7} + 0.4\overline{7}\) (bar on 7) in the form \( \frac{p}{q} \), where \(q \ne 0\). Solution: Step 1: Convert each decimal into fraction \[ 0.6 = \frac{6}{10} = \frac{3}{5}

Convert 0.12̅3 into Fraction (p/q) Express the Decimal \(0.12\overline{3}\) in the Form \( \frac{p}{q} \) Question: Express \(0.12\overline{3}\) (bar only on 3) in the form \( \frac{p}{q} \). Solution: Let \[ x = 0.12\overline{3} \] Multiply by 100 (to remove non-repeating part): \[ 100x = 12.\overline{3} \] Now multiply by 10 (since one digit repeats):

Convert 0.4̅7 into Fraction (p/q) Express the Decimal \(0.4\overline{7}\) in the Form \( \frac{p}{q} \) Question: Express \(0.4\overline{7}\) (bar only on 7) in the form \( \frac{p}{q} \). Solution: Let \[ x = 0.4\overline{7} \] Multiply by 10 (to move non-repeating part): \[ 10x = 4.\overline{7} \] Now multiply by 10 again (since one digit