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{57} ) on the number line?ExpertLevel 50Which coordinate represents \(\frac{\sqrt{121}-4}{7}\) on the number line?ExpertLevel 50If (x) lies between (-3) and (0) and its distance from (-3) is ( \frac{7}{5} ), what is (x)?ExpertLevel 50Which number is represented on the number line by \(\sqrt{\frac{169}{225}}\)?ExpertLevel 50Which value is greater than ( \sqrt{8}+\frac{1}{10} ) and less than (3)?ExpertLevel 50If A=-\sqrt{116}, B=-10.75, and C=-\frac{43}{4}, which point lies farthest to the left on the number line?ExpertLevel 50Which number has distance \(\sqrt{26}\) from 0 and lies to the right of 0 on the number line?EasyLevel 50Which statement is correct when comparing (4-\sqrt{6}) and ( \frac{31}{20} ) on the number line?ExpertLevel 50If ( \frac{a}{100} ) lies between ( \sqrt{2} ) and (1.42) on the number line, which value of (a) is possible?ExpertLevel 50Which is the simplest radical form of \(\sqrt{180}\) for locating it on the number line?ExpertLevel 50Which option gives the correct increasing order of ( -\sqrt{7} ), ( -2.64 ), and ( -\frac{53}{20} )?ExpertLevel 50If \(x=\sqrt{a}\) and \(11.3<x<11.4\), which value of \(a\) is possible?ExpertLevel 50Which is the most suitable estimate of ( \sqrt{11}-\sqrt{10} ) on the number line?ExpertLevel 50Which value lies between (-4) and ( -\sqrt{15} ) on the number line?ExpertLevel 50If point P is located at \\(\sqrt{196}-\sqrt{81}\\) on the number line, what is the coordinate of P?ExpertLevel 50On the number line, ( \frac{1}{\sqrt{25}} ) equals which point?ExpertLevel 50If the points \(A=-7.125\), \(B=-\sqrt{51}\), and \(C=-\frac{57}{8}\) are represented on the number line, which two points will lie at the same position?ExpertLevel 50On the number line, ( \sqrt{132} ) is closest to which integer?ExpertLevel 50If \(-\sqrt{82}<x<-9\) on the number line, which value is possible?MediumLevel 50What is the simplified form of ( \sqrt{19}+\sqrt{19}+\sqrt{19} ) on the number line?ExpertLevel 50