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Mathematics

Representing real numbers on the number line

संख्या रेखा पर वास्तविक संख्याओं का निरूपण

In this Class 10 Mathematics topic, students learn how real numbers—including rational numbers, irrational numbers and square roots—are located and represented accurately on the number line. They explore scale, order, distance and interval placement, and connect numerical values with geometric positions. This understanding supports the Polynomials chapter by helping students interpret and visualise real zeroes as points on the number line.

Practice questions

Which point on the number line represents the zero of the polynomial \(s(x)=5x-10\)?EasyLevel 51 How is a point representing an irrational real number shown on the number line?EasyLevel 51 Which point is (2.5) units to the right of (0) on the number line?EasyLevel 51 Which point is (1.75) units to the left of (0) on the number line?EasyLevel 51 On the number line, which point will be to the right, (\sqrt{2}) or (\sqrt{8})?EasyLevel 51 On the number line, which point will be to the right, (-\sqrt{3}) or (-\sqrt{12})?EasyLevel 51 Between which two integers will (\sqrt{15}) lie on the number line?EasyLevel 51 At which point will the zero of (u(x)=6x-18) lie on the number line?EasyLevel 51 To construct √2 on the number line, two perpendicular sides of a right triangle are each 1. What is the length of the hypotenuse?MediumLevel 49 Which fact can be used to place (\sqrt{5}) correctly on the number line?MediumLevel 49 To place (1.375) between (1) and (2) on the number line, how far should we move from (1)?MediumLevel 49 Between which two integers will (-\frac{7}{4}) lie on the number line?MediumLevel 49 If the part between (0) and (1) is divided into (8) equal parts, which point represents (\frac{5}{8})?MediumLevel 49 Between which two consecutive integers will (\sqrt{10}) be located on the number line?MediumLevel 49 To construct \(\sqrt{13}\) on the number line, if the perpendicular sides of a right triangle are 3 units and 2 units long, what is the length of its hypotenuse?MediumLevel 49 Which statement gives the correct position of (-\sqrt{4}) on the number line?MediumLevel 49 Which number lies between 2.6 and 2.7 on the number line?MediumLevel 49 Points \(A=-3\) and \(B=2\) lie on the number line. What is the distance from point \(A\) to point \(B\)?MediumLevel 49 If point P is 0.75 unit to the right of −1 on the number line, which number does P represent?MediumLevel 49 Write 0.4, 1/2, and 0.6 in the correct left-to-right order on the number line.EasyLevel 49