We need to draw a line segment AB of 2 unit on the number line. Then draw a perpendicular line segment BC at B of 1 units. Then join the points C and A, to form a line segment AC. According to Pythagoras Theorem
AC2 = AB2 + BC2
AC2 = 22 + 12
AC2 = 4 + 1 = 5
AC = \( \sqrt 5\)
Then draw the arc ACD, to get the number \( \sqrt 5\) on the number line.
Visualise the representation of \( 5.3\overline{7}\) on the number line upto 5 decimal places, that is upto 5.37777.
Visualise 2.665 on the number line, using successive magnification.
Find whether the following statements are true or false:
(i) Every real number is either rational or irrational.
(ii) π is an irrational number.
(iii) Irrational numbers cannot be represented by points on the number line.