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SubjectsMathematics
परिमेय संख्याएँ
In this Class 9 Mathematics topic from the Number Systems chapter, students explore rational numbers as numbers that can be written in the form p/q, where p and q are integers and q is not zero. They learn to represent and compare them on the number line, identify equivalent forms, and perform addition, subtraction, multiplication, and division. The topic also develops understanding of properties such as closure, commutativity, associativity, and distributivity, helping students apply rational numbers accurately in mathematical problems.
TOPIC PRACTICE
Up to 3 questions from this page. Select your focus, then start.
\(\frac{9}{4}\) is the ratio of two integers, 9 and 4, so it is rational. Its value is 2.25, which is not an integer. Both \(-4\) and \(\sqrt{16}=4\) are integers, whereas \(\sqrt{7}\) is irrational. Exam tip: first check whether a number can be written as \(\frac{p}{q}\), where \(p,q\) are integers and \(q\ne0\), then check whether its value is an integer.
View question details\(0.\overline{37}=0.373737\ldots\) is a recurring decimal, so it is a rational number. It can be written as \(\frac{37}{99}\), where both numerator and denominator are integers and the denominator is non-zero. In contrast, \(\sqrt{11}\) and \(\sqrt{13}\) are square roots of non-perfect squares and are irrational; \(\pi\) is also irrational. Exam tip: every terminating or recurring decimal is rational.
View question detailsBy definition, a rational number is written as \(\frac{m}{n}\), where both \(m\) and \(n\) are integers and \(n\ne0\). Therefore, integers is the correct option. “Natural numbers only” is incorrect because \(m\) can be zero or negative, as in \(-\frac{3}{5}\). Exam tip: in a rational number, the numerator and denominator are integers, but the denominator must not be zero.
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