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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

If \\(\sqrt{n}\\) lies between 9 and 10 on the number line, which value of n is possible?HardLevel 51 Which value lies between ( \frac{4}{9} ) and ( \frac{5}{9} ) on the number line?HardLevel 51 If (p=-\sqrt{17}) and (q=-4.2), which statement is correct on the number line?HardLevel 51 Which point is at distance ( \frac{11}{6} ) from ( \frac{3}{2} ) and lies to its left?HardLevel 51 Among (2.499), (2.51), (2.501), and (2.49), which is closest to (2.5) on the number line?HardLevel 51 To construct ( \sqrt{5} ) on the number line, what is the hypotenuse of a right triangle with perpendicular sides (2) and (1)?HardLevel 51 Which option correctly classifies (0.5151151115\ldots)?HardLevel 51 Which statement is correct when comparing ( \sqrt{7} ) and (2.65) on the number line?HardLevel 51 If \(a=\sqrt{75}\), then which of the following values is \(a-8\) closest to on the number line?HardLevel 51 Which value lies between ( -\sqrt{6} ) and (-2.4)?HardLevel 51 If A = -13/2 and B = -3/2, what is the midpoint on the number line?MediumLevel 51 Which statement is correct for ( \frac{355}{113} ) and ( \pi ) on the number line?HardLevel 51 Which option gives the correct decimal bound for ( \sqrt{30} )?HardLevel 51 If \(x=-5+\sqrt{22}\), in which interval does \(x\) lie on the number line?HardLevel 51 If \(r=0.375\), which simplest fraction represents \(r\) on the number line?HardLevel 51 Which value is ( \frac{7}{10} ) unit to the right of ( -\frac{5}{4} )?HardLevel 51 On the number line, ( \sqrt{98} ) is closest to which integer?HardLevel 51 If \(-\sqrt{m}\) lies between \(-3\) and \(-2\) on the number line, which value of \(m\) could be correct?HardLevel 51 What is the correct increasing order of 7/4, √3, and 1.76 on the number line?MediumLevel 51 If P = -√80, between which two consecutive integers is P located?MediumLevel 51