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
A student says that if the denominator of a fraction in simplest form has a prime factor other than 2 and 5, its decimal expansion is non-terminating recurring. Which of the following fractions supports the student's statement?MediumLevel 3A student says that the sum of two irrational numbers is always irrational. Which of the following examples disproves the statement?MediumLevel 3What is the value of \(\left(\sqrt{6.25}-\sqrt{0.64}\right)\)?MediumLevel 3What is the value of ( \sqrt{\frac{25}{49}}+\sqrt{\frac{16}{81}} )?MediumLevel 3What is the value of ( \sqrt{\frac{100}{169}}-\sqrt{\frac{9}{64}} )?MediumLevel 3Which option is an irrational number between (6) and (7)?MediumLevel 3Which is greater: \(\sqrt{63}\) or \(8\)?MediumLevel 3Between which two integers does ( \sqrt{101} ) lie?MediumLevel 3Between which two integers will ( \sqrt{130} ) lie?MediumLevel 3Which is greater between ( -\sqrt{65} ) and ( -8.1 )?MediumLevel 3What type of real number is 4.616161...?MediumLevel 3If (0.090090009...) has no regular repetition, what is it?MediumLevel 3What type of decimal expansion does \(\frac{37}{54}\) have?MediumLevel 3Which of the following numbers has a non-terminating, non-repeating decimal expansion?MediumLevel 3A student says that the decimal expansion of \(\frac{13}{375}\) will terminate because its denominator has 5 as a factor. What is the correct correction to the student's statement?MediumLevel 3A student says that the number 0.101001000100001... is rational because 0 occurs repeatedly in it. Which option is correct about this statement?MediumLevel 3Riya says that the sum of any two irrational numbers is always irrational. Which of the following examples disproves her statement?MediumLevel 3What is the value of ( \frac{4+\sqrt{3}}{4-\sqrt{3}} ) after rationalising?MediumLevel 3What will be the denominator after rationalising ( \frac{\sqrt{11}+3}{\sqrt{11}-3} )?MediumLevel 3A student says, “A number with an infinite decimal expansion is always irrational.” Which of the following examples proves that the student's statement is incorrect?MediumLevel 3