May 2026

Convert 0.4 Bar into Fraction MCQ Question The value of \(0.\overline{4}\) in the form \( \frac{p}{q} \), where \(q \neq 0\), is: (a) \( \frac{4}{9} \) (b) \( \frac{2}{5} \) (c) \( \frac{1}{5} \) (d) \( \frac{4}{5} \) Solution Let \( x = 0.\overline{4} \) Then, \[ x = 0.4444\ldots \] Multiply both sides by […]

Irrational Number from Decimal Expansion MCQ Question Which of the following is an irrational number? (a) 0.13 (b) 0.1315 (c) 0.1315 (d) 0.301323100523 … Solution Option (a): 0.13 ✘ Rational This is a terminating decimal, so it is rational. Option (b): 0.1315 ✘ Rational This is also a terminating decimal, hence rational. Option (c): 0.1315

Decimal Representation of Irrational Numbers MCQ Question A number is irrational if and only if its decimal representation is: (a) non-terminating (b) non-terminating and repeating (c) non-terminating and non-repeating (d) terminating Solution An irrational number cannot be expressed in the form \( \frac{p}{q} \). Its decimal expansion has two important properties: It is non-terminating (never

Decimal Expansion of Rational Numbers MCQ Question The decimal expansion of a rational number is: (a) terminating or non-terminating non-repeating (b) terminating or non-terminating repeating (c) terminating and repeating (d) none of these Solution A rational number can be written in the form \( \frac{p}{q} \), where \( q \neq 0 \). Its decimal expansion

Which Statements are Correct in Number System? Question Which of the following statements is/are correct? (i) Every integer is a rational number (ii) Every rational number is an integer (iii) A real number is either rational or irrational number (iv) Every whole number is a natural number Options: (a) (ii) (b) (iii) (c) (i) and

MCQ Numbers Between 7 and 11 Numbers Between 7 and 11 in the Form \( \frac{m}{6} \) Options: (a) 42 and 60 (b) 42 and 66 (c) 42 and 77 (d) 48 and 60 Solution: Given: \[ 7 < \frac{m}{6} < 11 \] Multiply by 6: \[ 42 < m < 66 \] Thus, integer

MCQ on 0.3̅ Rational or Irrational Which of the Following is True About \(x = 0.\overline{3}\)? Options: (a) x is a rational number, because \(10x = 3 + x\) (b) x is a rational number, because \(10x = 3 – x\) (c) x is an irrational number, because \(10x = 3 + x\) (d) x

Classification of Real Numbers Classification of Real Numbers Fill in the Blank: Every real number is either rational or irrational number. Explanation: Real numbers include all numbers on the number line. These are classified into: Rational numbers (can be written as \( \frac{p}{q} \)) Irrational numbers (cannot be written as \( \frac{p}{q} \)) Final Answer:

Sum of Rational and Irrational Number Sum of a Rational and an Irrational Number Fill in the Blank: The sum of a rational number and an irrational number is an irrational number. Explanation: Adding a rational number to an irrational number always gives an irrational result. Example: \[ 2 + \sqrt{3} = 3.732\ldots \] Final

Sum of Recurring Decimals Sum of Recurring Decimals Fill in the Blank: \(0.\overline{3} + 0.\overline{4} = \) \(0.\overline{7}\) Explanation: \[ 0.\overline{3} = \frac{1}{3}, \quad 0.\overline{4} = \frac{4}{9} \] \[ \frac{1}{3} = \frac{3}{9} \] \[ \frac{3}{9} + \frac{4}{9} = \frac{7}{9} \] \[ \frac{7}{9} = 0.\overline{7} \] Final Answer: \(0.\overline{7}\) Next Question / Full Exercise