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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.
In 0.272727\ldots, the block 27 repeats continuously, so it is a non-terminating recurring decimal and therefore a rational number. In fact, \(0.272727\ldots=\frac{27}{99}=\frac{3}{11}\). It is not a terminating decimal and it is not an integer. Exam tip: A decimal that terminates or repeats a fixed block of digits is rational.
\(\frac{5}{8}\) is a ratio of two integers, and \(-7\) can be written as \(\frac{-7}{1}\); therefore, both are rational numbers. \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\), \(\sqrt{11}\), and \(\pi\) are irrational, while \(0.101001\ldots\) is a non-terminating, non-repeating decimal. Exam tip: A number is rational if it can be written as \(\frac{p}{q}\), where \(p,q\) are integers and \(q\ne0\).
-12 is an integer. It can be written as \(\frac{-12}{1}\), so it is also a rational number. \(\frac{3}{7}\) is rational but not an integer, while \(\sqrt{15}\) and \(\pi\) are irrational. Exam tip: To check whether an integer is rational, write it as a fraction with denominator 1.
QUIZ COMPLETE
