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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.3
Question 1.
Represent the following irrational numbers on the number line.
(i) \(\sqrt { 3}\)
(ii) \(\sqrt { 4.7 }\)
(iii) \(\sqrt { 6.5 }\)
Solution:
(i) \(\sqrt { 3}\)
(i) Draw a line and mark a point A on it.
(ii) Mark a point B such that AB = 3 cm.
(iii) Mark a point C on this line such that BC = 1 unit.
(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O.
(v) With O as center and OC = OA as radius, draw a semicircle.
(vi) Draw a line BD, which is perpendicular to AB at B.
(vii) Now BD = \(\sqrt { 3}\), which can be marked in the number line as the value of BE = BD = \(\sqrt { 3}\)
(ii) \(\sqrt { 4.7 }\)
(i) Draw a line and mark a point A on it.
(ii) Mark a point B such that AB = 4.7 cm.
(iii) Mark a point C on this line such that BC = 1 unit.
(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O.
(v) With O as center and OC = OA as radius, draw a semicircle.
(vi) Draw a line BD, which is perpendicular to AB at B.
(vii) Now BD = \(\sqrt { 4.7 }\), which can be marked in the number line as the value of BE = BD = \(\sqrt { 4.7 }\)
(iii) \(\sqrt { 6.5 }\)
(i) Draw a line and mark a point A on it.
(ii) Mark a point B such that AB = 6.5 cm.
(iii) Mark a point C on this line such that BC = 1 unit.
(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O.
(v) With O as center and OC = OA as radius, draw a semicircle.
(vi) Draw a line BD, which is perpendicular to AB at B.
(vii) Now BD = \(\sqrt { 6.5 }\), which can be marked in the number line as the value of BE = BD = \(\sqrt { 6.5 }\).
Question 2.
Find any two irrational numbers between
(i) 0.3010011000111…. and 0.3020020002….
(ii) \(\frac { 6 }{ 7 }\) and \(\frac { 12 }{ 13 }\)
(iii) \(\sqrt { 2}\) and \(\sqrt { 3}\)
Solution:
(i) 0.3010011000111…. and 0.3020020002….
Two irrational numbers 0.301202200222 …., 0.301303300333…..
(ii) \(\frac { 6 }{ 7 }\) and \(\frac { 12 }{ 13 }\)
\(\frac { 6 }{ 7 }\) = 0.857142…
\(\frac { 12 }{ 13 }\) = 0.923076
Two irrational numbers between 0.8616611666111……, 0.8717711777111…..
(iii) \(\sqrt { 2}\) and \(\sqrt { 3}\)
\(\sqrt { 2 }\)= 1.414……
\(\sqrt { 3}\) = 1.732….
∴ Two irrational numbers between 1.5155…., 1.6166…….
Question 3.
Find any two rational numbers between 2.2360679….. and 2.236505500….
Solution:
Any two rational numbers are 2.2362, 2.2363