May 2026

Sum of 0.23 Bar and 0.22 Bar Question The value of \(0.\overline{23} + 0.\overline{22}\) is: (a) 0.45 (b) 0.43 (c) 0.54 (d) 0.45 Solution Convert recurring decimals into fractions: \[ 0.\overline{23} = \frac{23}{99} \] \[ 0.\overline{22} = \frac{22}{99} \] Add them: \[ \frac{23}{99} + \frac{22}{99} = \frac{45}{99} \] Simplify: \[ \frac{45}{99} = \frac{5}{11} \] Convert […]

Convert 0.01 Bar into Fraction MCQ Question The number \(0.\overline{01}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{1}{1000} \) (b) \( \frac{1}{100} \) (c) \( \frac{1}{1999} \) (d) \( \frac{1}{99} \) Solution Let \( x = 0.\overline{01} = 0.010101\ldots \) Multiply both sides by 100: \[ 100x

Convert 23.43 Bar into Fraction MCQ Question The number \(23.\overline{43}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{2320}{99} \) (b) \( \frac{2343}{100} \) (c) \( \frac{2343}{999} \) (d) \( \frac{2320}{199} \) Solution Let \( x = 23.\overline{43} = 23.434343\ldots \) Multiply by 100: \[ 100x = 2343.4343\ldots

Convert 0.32 Bar into Fraction MCQ Question The number \(0.3\overline{2}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{8}{25} \) (b) \( \frac{29}{90} \) (c) \( \frac{32}{99} \) (d) \( \frac{32}{199} \) Solution Let \( x = 0.3\overline{2} = 0.32222\ldots \) Multiply by 10: \[ 10x = 3.2222\ldots

Convert 0.3 Bar into Fraction MCQ Question The number \(0.\overline{3}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{33}{100} \) (b) \( \frac{3}{10} \) (c) \( \frac{1}{3} \) (d) \( \frac{3}{100} \) Solution Let \( x = 0.\overline{3} \) \[ x = 0.3333\ldots \] Multiply both sides by

Convert 1.27 Bar into Fraction MCQ Question The number \(1.\overline{27}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{14}{9} \) (b) \( \frac{14}{11} \) (c) \( \frac{14}{13} \) (d) \( \frac{14}{15} \) Solution Let \( x = 1.\overline{27} \) \[ x = 1.272727\ldots \] Multiply both sides by

Irrational Number from Decimal Expansion MCQ Question Which of the following is irrational? (a) 0.15 (b) 0.01516 (c) 0.1516 (d) 0.5015001500015.. Solution Option (a): 0.15 ✘ Rational Terminating decimal → rational number. Option (b): 0.01516 ✘ Rational Terminating decimal → rational number. Option (c): 0.1516 ✘ Rational Terminating decimal → rational number. Option (d): 0.5015001500015..

Number Line and Real Numbers MCQ Question Every point on number line represents: (a) a unique real number (b) a natural number (c) a rational number (d) an irrational number Solution The number line includes all types of numbers: Natural numbers Integers Rational numbers Irrational numbers Together, these form the set of real numbers. Each

Non-Terminating Repeating Decimal MCQ Question Which of the following numbers can be represented as non-terminating repeating decimals? (a) \( \frac{39}{24} \) (b) \( \frac{3}{16} \) (c) \( \frac{3}{11} \) (d) \( \frac{137}{25} \) Solution A rational number \( \frac{p}{q} \) has: Terminating decimal if \( q \) has only prime factors 2 and/or 5 Non-terminating

Square Root of Natural Number MCQ Question If \( n \) is a natural number, then \( \sqrt{n} \) is: (a) always a natural number (b) always a rational number (c) always an irrational number (d) sometimes a natural number and sometimes an irrational number Solution If \( n \) is a perfect square (like