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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

If the decimal expansion of a real number is non-terminating and non-recurring, what type of number is it?HardLevel 1Which is greater between ( -\sqrt{30} ) and ( -\frac{11}{2} )?HardLevel 1What will be the decimal expansion of the simplified form of ( \frac{39}{312} )?HardLevel 1What will be the decimal expansion of the simplified form of ( \frac{22}{77} )?HardLevel 1Which of the following numbers has a non-terminating recurring decimal expansion?HardLevel 1How will (5.232323...) be classified as a real number?HardLevel 1What is the simplest form of \(\sqrt{3}+\sqrt{12}+\sqrt{27}+\sqrt{48}\)?HardLevel 1What is the value of \( \left(\frac{1}{\sqrt{5}-2}\right)-\left(\frac{1}{\sqrt{5}+2}\right) \)?HardLevel 1What is the value of \(\frac{1}{3-\sqrt7}+\frac{1}{3+\sqrt7}\)?MediumLevel 1Reema claims that the decimal expansion of \(\frac{13}{120}\) will terminate because 120 has both 2 and 5 as factors. Which option correctly identifies the error in Reema’s statement?HardLevel 1What is the value of √12 + √75 − √48 − √27?MediumLevel 1If \(a=\sqrt{3}+\sqrt{2}\), what is the value of \(a^2+\frac{1}{a^2}\)?HardLevel 1If \(x=\sqrt5+2\), what is the value of \(x+\frac1x\)?MediumLevel 1If \(x=-7\), what is the value of \(\sqrt{x^2}-2x\)?HardLevel 1What is the correct simplified form of ( |3-\sqrt{20}| )?HardLevel 1Which of the following statements is not always true?HardLevel 1What is the correct statement about ( \sqrt{27}+\sqrt{12} ) and ( \sqrt{75} )?HardLevel 1A student says that \(0.1010010001\ldots\) is a rational number because it contains only the digits 0 and 1. Why is the student's statement incorrect?HardLevel 1What is the value of 1/(√3 − √2) − 1/(√3 + √2)?HardLevel 5What is the value of \(\frac{1}{\sqrt{11}+3}+\frac{1}{\sqrt{11}-3}\)?HardLevel 1