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Subjects

Mathematics

Real Numbers

वास्तविक संख्याएँ

Real Numbers is a Class 9 Mathematics topic in the Number Systems chapter. Students learn how rational and irrational numbers together form the real number system, represent them on the number line, and distinguish between their decimal expansions. The topic develops understanding of terminating and non-terminating decimals, recurring and non-recurring forms, and the key properties of real numbers under addition, subtraction, multiplication, and division. It also builds a foundation for working confidently with numbers in algebra and geometry.

Practice questions

Which option contains only irrational real numbers?EasyLevel 5A student considers the number 0.101001000100001… rational because it contains only the digits 0 and 1. What is the correct evaluation of this statement?EasyLevel 5What is obtained by rationalising the denominator of ( \frac{1}{\sqrt{5}} )?EasyLevel 5What is the form of ( \frac{2}{\sqrt{3}} ) with rational denominator?EasyLevel 5Which is greater between ( \sqrt{2} ) and ( \sqrt{3} )?EasyLevel 5Which is greater between ( -\sqrt{5} ) and ( -2 )?EasyLevel 5Which of the two numbers frac{3}{4} and sqrt{1} is greater?EasyLevel 5How many rational numbers are there between any two distinct real numbers?EasyLevel 5Which is an irrational number between (2) and (3)?EasyLevel 5What is the value of \(\sqrt{0.04}\)?EasyLevel 5What is the value of \(\sqrt{0.25}\)?EasyLevel 5What is the value of \(\sqrt{\frac{49}{64}}\)?EasyLevel 5What is \(\sqrt{\frac{16}{81}}\) equal to?EasyLevel 5What type of number is ( (2+\sqrt{3}) )?EasyLevel 5What type of number is ( (5-\sqrt{2}) )?EasyLevel 5What is the value of ( \sqrt{7}\times\sqrt{7} )?EasyLevel 5A student says that 0.125 is an irrational number because it has decimal digits. What is the error in the student's statement?EasyLevel 5A student considers the number 0.101001000100001... to be rational because its decimal expansion consists of digits. Which is the correct evaluation of this conclusion?EasyLevel 6Between which two integers does ( \sqrt{11} ) lie on the number line?EasyLevel 6What is the simplified surd form of \(\sqrt{98}\)?EasyLevel 6