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 option gives the correct decimal bound for \(\sqrt{24}\) on the number line?ExpertLevel 49Which point on the number line is represented by \(\frac{\sqrt{64}-3}{5}\)?ExpertLevel 49If (x) lies between (-2) and (1) and its distance from (-2) is ( \frac{5}{4} ), what is (x)?ExpertLevel 49On the number line, ( \sqrt{\frac{49}{121}} ) is equal to what?ExpertLevel 49Which of the following values is greater than \(\sqrt{3}+\frac{1}{4}\) and less than \(2\)?ExpertLevel 49If \(A=-\sqrt{28}\), \(B=-5.3\), and \(C=-\frac{16}{3}\), which of these numbers is located farthest to the left on the number line?ExpertLevel 49Which number has distance √17 from 0 and lies to the left of 0 on the number line?EasyLevel 49Which statement is correct when comparing \(3-\sqrt{2}\) and \(\frac{8}{5}\) on the number line?ExpertLevel 49If ( \frac{a}{10} ) lies between ( \sqrt{2} ) and (1.5) on the number line, which integer value of (a) is possible?ExpertLevel 49Which is the simplest form of (\sqrt{80}) for understanding its position on the number line?ExpertLevel 49Which option gives the correct increasing order of ( -\sqrt{2} ), ( -1.42 ), and ( -\frac{7}{5} )?ExpertLevel 49If the coordinate of a point on the number line is \\(x=\\sqrt{a}\\) and \\(5.2<x<5.3\\), which value of \\(a\\) is possible?ExpertLevel 49Which is the most suitable estimate of ( \sqrt{7}-\sqrt{5} ) on the number line?ExpertLevel 49Which value lies between (-2) and ( -\sqrt{3} ) on the number line?ExpertLevel 49If the point \(P\) on the number line represents the number \(\sqrt{49}+\sqrt{16}\), what is the coordinate of \(P\)?ExpertLevel 49On the number line, what point is equal to \(\frac{1}{\sqrt{4}}\)?EasyLevel 49If \(A=-6.25\), \(B=-\sqrt{39}\), and \(C=-\frac{25}{4}\), which two of the points \(A\), \(B\), and \(C\) represent the same real number on the number line?ExpertLevel 49On the number line, ( \sqrt{90} ) is closest to which integer?ExpertLevel 49If \(x\) on the number line satisfies \(-\sqrt{50}<x<-7\), which value is possible?MediumLevel 49What is the simplified form of ( \sqrt{13}+\sqrt{13} ) on the number line?ExpertLevel 49