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
In which interval is (2-\sqrt{10}) correctly located on the number line?ExpertLevel 49If \(m\) is an integer such that \(m<\sqrt{57}<m+1\), what is the value of \(m\)?ExpertLevel 49Which point on the number line is represented by \( -\sqrt{0.36} \)?ExpertLevel 49If \(x=\frac{\sqrt{81}}{4}\), which value correctly represents \(x\) on the number line?ExpertLevel 49Which statement is correct for ( \sqrt{5} ) and (2.24) on the number line?ExpertLevel 49If point \(C\) lies \(\sqrt{6}\) units to the left of the point \(-1\) on the number line, what is the coordinate of \(C\)?ExpertLevel 49Which point is exactly midway between ( \frac{2}{5} ) and ( \frac{3}{5} ) on the number line?ExpertLevel 49Which value lies between −√3 and −5/3 on the number line?MediumLevel 49If (a=\sqrt{27}-\sqrt{12}), what is the simplified form of (a) on the number line?ExpertLevel 49What type of number is 0.2727727772… on the number line? Here, the number of 7s following each 2 in the decimal expansion keeps increasing.ExpertLevel 49If \(\sqrt{n}\) lies between 6.4 and 6.5 on the number line, which value of \(n\) can be correct?ExpertLevel 49Between which two consecutive integers does \(-\frac{17}{5}\) lie on the number line?ExpertLevel 49On the number line, points \(A=-2.75\) and \(B=1.25\) are given. What is the midpoint of the line segment \(AB\)?ExpertLevel 49Which is the correct value of \(\sqrt{0.0081}\) to represent on the number line?ExpertLevel 49Between which two consecutive integers does \\(\sqrt{37}+1\\) lie on the number line?ExpertLevel 49If \(p=2-\sqrt{45}\), in which of the following intervals does \(p\) lie on the number line?ExpertLevel 49Which point is 3/20 unit to the left of 7/10?EasyLevel 49Which decimal value is closest to √63 on the number line?MediumLevel 49If ca(a=\sqrt{8}), ca(b=\frac{14}{5}), and ca(c=2.81), which of these numbers is greatest on the number line?ExpertLevel 49Which option gives the correct decimal bound for \(\sqrt{24}\) on the number line?ExpertLevel 49