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SubjectsMathematics
संख्या रेखा
The Number Line topic in Class 9 Mathematics, within Number Systems, helps students visualise numbers as points on a continuous line. They learn to locate and compare integers, rational numbers, irrational numbers and real numbers, understand their order and relative position, and interpret distance using intervals. The topic also supports the geometric representation of irrational numbers such as √2, making the connection between numerical expressions and their positions on the real number line clear.
Correct answer: B. (\frac{19}{6})
Explanation: Distance equals the absolute difference of the two coordinates. In exams, treat the negative sign as direction, not distance.
Correct answer: B. (7) and (8)
Explanation: Since (7^2=49) and (8^2=64), (\sqrt{52}) lies between them. In exams, locate square roots by comparing squares.
Correct answer: B. 0.75
Explanation: The coordinate of the midpoint is the average of the coordinates of the two endpoints. Thus, \(\frac{-1.25+2.75}{2}=\frac{1.50}{2}=0.75\). Therefore, option B is correct. Option A, 0.50, results from an arithmetic error in adding or averaging the coordinates. Exam tip: Add the endpoint coordinates and divide the sum by 2 to find the midpoint.
Correct answer: A. (-4) and (-3)
Explanation: Since (\sqrt{10}) lies between (3) and (4), (-\sqrt{10}) lies between (-4) and (-3). In exams, place negative surds to the left.
Correct answer: A. (-2) and (8)
Explanation: Distance means (x=3\pm5), so the values are (-2) and (8). In exams, always consider both directions.
Correct answer: C. Irrational number
Explanation: This decimal is non-recurring and non-terminating, so it is irrational. In exams, identify non-recurring infinite decimals as irrational.
Correct answer: A. It is between (2) and (3) at (2.75)
Explanation: (\frac{11}{4}=2.75), so it lies between (2) and (3). In exams, convert fractions to decimals or mixed numbers for placement.
Correct answer: B. (-2.45)
Explanation: (-\frac{5}{2}=-2.5), and (-2.45) is greater than (-2.5) but less than (-2.4). In exams, compare negative numbers carefully.
Correct answer: C. (0.7)
Explanation: The direct answer is option C,
\(0.7\). On a number line, moving left means moving to a smaller number, so subtract the distance from the starting number:
\(a=1.6-0.9=0.7\). We can check it because the distance from
\(0.7\) to
\(1.6\) is
\(1.6-0.7=0.9\), and
\(0.7\) is indeed on the left. Option A,
\(2.5\), is obtained by adding and lies to the right, so it is wrong. Option B,
\(0.9\), is the distance moved, not the final coordinate. Option C is correct because it is the starting value minus the leftward distance. Option D,
\(-0.7\), subtracts too much and is not 0.9 units left of 1.6; its distance is
\(2.3\). Exam cue: right means add, left means subtract.
Correct answer: C. (C)
Explanation: (-\frac{4}{5}=-0.8), which is the smallest among the given values. In exams, the farthest-left number is the least number.
Correct answer: B. (-\frac{1}{3})
Explanation: From (x^2=\frac{1}{9}), (x=\pm\frac{1}{3}), and the given interval needs the negative value. In exams, use conditions to choose the correct sign.
Correct answer: A. Because the hypotenuse is (\sqrt{1^2+1^2}=\sqrt{2})
Explanation: By Pythagoras theorem, the hypotenuse is (\sqrt{2}). In exams, transfer the hypotenuse length to the number line for surd construction.
Correct answer: C. (\frac{5}{14})
Explanation: The middle number is the average, so (\frac{\frac{2}{7}+\frac{3}{7}}{2}=\frac{5}{14}). In exams, find the mean for the midway value.
Correct answer: B. 4.4
Explanation: The distance between two points on a number line is the absolute value of the difference of their coordinates. Thus, \(MN=|-1.8-(-6.2)|=|-1.8+6.2|=4.4\). Therefore, 4.4 is correct. A value such as 3.4 can result from handling the negative signs incorrectly. Exam tip: distance or length is always positive.
Correct answer: B. (4)
Explanation: (\sqrt{18}\approx4.24), so the nearest integer is (4). In exams, first locate it between consecutive squares.
Correct answer: A. Every real number has a unique point
Explanation: The number line represents real numbers, and each real number has a unique position. In exams, connect the number line with real numbers.
Correct answer: A. (\frac{1}{2})
Explanation: The equidistant point is the midpoint, so (\frac{-3+4}{2}=\frac{1}{2}). In exams, use the average for equidistant points.
Correct answer: C. (\sqrt{\frac{1}{2}})
Explanation: (\sqrt{\frac{1}{2}}) lies between (0) and (1) and cannot be simplified to a rational form. In exams, identify square roots of non-perfect squares as irrational.
Correct answer: C. (0.003)
Explanation: A positive number is greater than all negative numbers, so (0.003) is the greatest. In exams, the number to the right is greater.
Correct answer: B. Into (8) equal parts and take the (5)th point
Explanation: In (\frac{5}{8}), the denominator is (8), so divide the unit into (8) equal parts and take the (5)th. In exams, the denominator gives the number of equal parts.
Correct answer: B. Left of (9)
Explanation: (\sqrt{80}\approx8.94), so it lies slightly left of (9). In exams, connect approximation with direction near the nearest integer.
Correct answer: B. (-\sqrt{5})
Explanation: The approximate values are (-2.25), (-2.2), (-2.236), and (-2.3); from the right, (-2.2) comes first and (-\sqrt{5}) second. In exams, order negative decimals using approximation.
Correct answer: B. (b) is to the right of (a)
Explanation: On the number line, the greater number lies to the right, so (b) is to the right of (a). In exams, connect inequalities with direction.
Correct answer: A. \(\sqrt{7}\)
Explanation: \(\sqrt{7}\) is irrational because 7 is not a perfect square. Its decimal expansion is non-terminating and non-repeating, but it is a real number, so it has a unique point on the number line. Exam tip: the square root of a non-perfect square is irrational.
Correct answer: B. \(\sqrt{10}\)
Explanation: Since \(3^2=9\) and \(4^2=16\), and \(9<10<16\), we get \(3<\sqrt{10}<4\). Hence, \(\sqrt{10}\) is the correct option. \(\sqrt{8}<3\), while both \(\sqrt{17}\) and \(\sqrt{20}\) are greater than 4. Exam tip: locate a square root by comparing the number inside it with nearby perfect squares.
