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
If c(csqrt{n}c) lies between 8.4 and 8.5 on the number line, which value of n can be correct?ExpertLevel 51Between which two integers is ( -\frac{43}{11} ) located on the number line?ExpertLevel 51If point A has coordinate \(-4.125\) and point B has coordinate \(1.875\) on the number line, what is the midpoint of segment AB?ExpertLevel 51What is the coordinate of the point represented by \(\sqrt{0.0225}\) on the number line?ExpertLevel 51Between which two consecutive integers does \(\sqrt{131}+2\) lie on the number line?ExpertLevel 51If \(p=4-\sqrt{99}\), in which of the following intervals does \(p\) lie on the number line?ExpertLevel 51Which point is ( \frac{5}{18} ) unit to the left of ( \frac{11}{12} )?ExpertLevel 51Which decimal value is closest to √199 on the number line?MediumLevel 51If \(a=\sqrt{26}\), \(b=\frac{51}{10}\), and \(c=5.11\), which of these numbers will lie farthest to the right on the number line?ExpertLevel 51Which option gives the correct decimal bound for ( \sqrt{86} ) on the number line?ExpertLevel 51Which point on the number line has the coordinate \(\frac{\sqrt{225}-6}{9}\)?ExpertLevel 51If (x) lies between (-5) and (-1) and its distance from (-5) is ( \frac{13}{6} ), what is (x)?ExpertLevel 51Which number is represented by \(\sqrt{\frac{196}{289}}\) on the number line?ExpertLevel 51Which value is greater than ( \sqrt{15}+\frac{1}{8} ) and less than (4)?ExpertLevel 51If \(A=-\sqrt{185}\), \(B=-13.6\), and \(C=-\frac{68}{5}\), which point lies farthest to the left on the number line?ExpertLevel 51Which number has distance \(\sqrt{41}\) from 0 and lies to the left of 0 on the number line?EasyLevel 51Which statement is correct when comparing (5-\sqrt{11}) and ( \frac{17}{10} ) on the number line?ExpertLevel 51If ( \frac{a}{100} ) lies between ( \sqrt{3} ) and (1.74) on the number line, which value of (a) is possible?ExpertLevel 51Which is the simplest form of \(\sqrt{245}\) for understanding its position on the number line?ExpertLevel 51Which option gives the correct increasing order of ( -\sqrt{13} ), ( -3.61 ), and ( -\frac{18}{5} )?ExpertLevel 51