May 2026

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

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}