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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 value lies between ( \sqrt{33} ) and ( \sqrt{34} ) on the number line?ExpertLevel 50 In which interval is (5-\sqrt{31}) correctly located on the number line?ExpertLevel 50 If m is an integer and \(m<\sqrt{145}<m+1\), what is the value of m?ExpertLevel 50 Which number does \(-\sqrt{1.69}\) represent on the number line?ExpertLevel 50 If \(x=\frac{\sqrt{144}}{5}\), which number represents \(x\) on the number line?ExpertLevel 50 Which statement is correct for ( \sqrt{15} ) and (3.88) on the number line?ExpertLevel 50 If point (C) is ( \sqrt{19} ) units to the left of (2), what is the coordinate of (C)?ExpertLevel 50 Which point is exactly midway between \(\frac{5}{12}\) and \(\frac{7}{12}\) on the number line?EasyLevel 50 Which value lies between ( -\sqrt{10} ) and ( -\frac{19}{6} ) on the number line?ExpertLevel 50 If (a=\sqrt{75}-\sqrt{27}), what is the simplified form of (a) on the number line?ExpertLevel 50 What type of number is (0.6161161116\ldots) on the number line?ExpertLevel 50 If \(\sqrt{n}\) lies between \(7.2\) and \(7.3\) on the number line, which value of \(n\) is possible?ExpertLevel 50 Between which two integers is ( -\frac{31}{9} ) located on the number line?ExpertLevel 50 If point A has coordinate −3.25 and point B has coordinate 2.75 on the number line, what is the midpoint of line segment AB?ExpertLevel 50 Which of the following numbers represents an irrational point lying between 3 and 4 on the number line?ExpertLevel 50 Between which two consecutive integers does \(\sqrt{89}+1\) lie on the number line?ExpertLevel 50 If \(p=-\sqrt{68}+3\), in which interval will \(p\) lie on the number line?ExpertLevel 50 Which point is ( \frac{7}{25} ) unit to the left of ( \frac{9}{10} )?ExpertLevel 50 Which decimal value is closest to ( \sqrt{143} ) on the number line?ExpertLevel 50 If (a=\sqrt{17}), (b=\frac{33}{8}), and (c=4.13), which number will be farthest to the right on the number line?ExpertLevel 50