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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: A. 14
Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(\left|-15-(-1)\right|=|-14|=14\). Therefore, the correct answer is 14. A value such as 13 results from incorrect subtraction. Exam tip: a distance is always non-negative.
Correct answer: A. The student's conclusion is correct; \(\sqrt{7}\) lies between 2 and 3 and is closer to 3.
Explanation: Since \(2^2=4\) and \(3^2=9\), \(\sqrt{7}\) lies between 2 and 3. Also, \(\sqrt{7}\approx2.646\), so its distance from 3 is about 0.354, less than 0.646 from 2. Thus option B is wrong. Exam tip: compare nearby perfect squares first.
Correct answer: A. -12
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-6+(-18)}{2}=\frac{-24}{2}=-12\). Therefore, the correct answer is \(-12\). Although \(-11\) may seem close, it is not equally distant from both numbers. Exam tip: include the signs of negative numbers while adding them for a midpoint.
Correct answer: A. 60
Explanation: The distance between two numbers on a number line is the absolute value of their difference. Thus, \(|10-(-50)|=|60|=60\). Although \(-60\) can arise as a signed difference in the reverse order, a distance can never be negative. Exam tip: always take the absolute value of the difference when finding distance.
Correct answer: B. -0.00201
Explanation: For negative numbers, the number closer to zero is greater. Here, \(-0.00201 > -0.00210\) because \(-0.00201\) is closer to zero. Writing \(-0.0021\) as \(-0.00210\) makes the comparison clear. Exam tip: Add trailing zeros when needed to compare the same number of decimal places.
Correct answer: A. \(8\)
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-4+20}{2}=\frac{16}{2}=8\). Therefore, the correct answer is \(8\). \(10\) would be the midpoint of 0 and 20, so it is not correct here. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: A. 20
Explanation: On a number line, the distance between two numbers is the absolute value of their difference: \(\lvert -25-(-5)\rvert=\lvert -20\rvert=20\). Therefore, the correct answer is 20. A value such as 15 can result from incorrect subtraction. Exam tip: distance is always non-negative.
Correct answer: B. \(-0.506\)
Explanation: Write \(-0.56\) as \(-0.560\) to compare the decimals easily. Since \(-0.506\) is closer to zero than \(-0.560\), it is greater; among negative numbers, the number closer to zero is greater. Therefore, \(-0.506\) is the correct answer. Exam tip: Make the number of decimal places equal before comparing decimals.
Correct answer: A. \(-2\)
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-9+5}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is correct. \(-1\) is not correct because it is not at an equal distance from \(-9\) and \(5\). Exam tip: Add the two numbers and divide by 2 to find their midpoint.
Correct answer: A. 8
Explanation: On a number line, the distance between two numbers is the absolute value of their difference: \(|-12-(-20)|=|-12+20|=|8|=8\). Therefore, the correct answer is 8. A value such as 7 can result from an incorrect subtraction, and distance can never be negative. Exam tip: always use \(|a-b|\) to find the distance between two numbers.
Correct answer: B. -0.71
Explanation: For comparison, write -0.71 as -0.710. Between -0.710 and -0.701, -0.710 is more negative, so it lies further left on the number line and is smaller. Therefore, -0.71 is correct. -0.701 is greater because it is closer to zero. Exam tip: Among negative decimals, the number with the greater magnitude is smaller.
Correct answer: A. \(-10\)
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-3+(-17)}{2}=\frac{-20}{2}=-10\). Therefore, \(-10\) is correct. \(-9\) is not correct because it is not equally distant from \(-3\) and \(-17\). Exam tip: when adding negative numbers, add their magnitudes and keep the negative sign.
Correct answer: A. 30
Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(\left|-45-(-15)\right|=\left|-30\right|=30\). Therefore, the correct answer is 30. \(-30\) can be the signed difference, but distance can never be negative. Exam tip: always take the absolute value when finding distance.
Correct answer: B. Infinitely many rational numbers
Explanation: The correct answer is infinitely many rational numbers. The midpoint \(\frac{a+b}{2}\) is rational and lies between \(a\) and \(b\). Repeatedly taking midpoints produces endlessly many rational numbers. Exam tip: between any two distinct rational numbers, rationals are always infinite.
Correct answer: A. 30
Explanation: On a number line, the distance between two numbers is the absolute value of their difference. Thus, \(\lvert -60-(-30)\rvert=\lvert -30\rvert=30\). Therefore, the correct answer is 30. \(-30\) is the signed difference, not the distance, because distance cannot be negative. Exam tip: always use the absolute value of the difference when finding distance.
Correct answer: B. \(-1\)
Explanation: For negative numbers, the number closer to zero is greater. Since \(-1\) is closer to zero than \(-1.1\), \(-1 > -1.1\). Option \(-1.1\) is smaller because it lies further left on the number line. Exam tip: While comparing negative decimals, remember that a larger magnitude means a smaller number.
Correct answer: B. ( -0.06 )
Explanation: -0.06 is greater than -0.6 because it lies closer to zero and to the right on the number line. In fact, -0.6 = -0.60, and -0.06 > -0.60. Option A is more negative, so it is smaller. Exam tip: when comparing negative decimals, the number closer to zero is greater.
Correct answer: A. 1
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-11+13}{2}=\frac{2}{2}=1\). Therefore, 1 is correct. Zero is not equally distant from the two numbers: it is 11 units from -11 and 13 units from 13. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: A. 12
Explanation: On a number line, the distance between two numbers is the absolute value of their difference: \(\lvert -7-(-19)\rvert=\lvert 12\rvert=12\). Therefore, the correct answer is 12. Values such as 11 or 13 result from subtracting incorrectly by one; they are not the actual difference. Exam tip: always express distance as a non-negative value.
Correct answer: B. ( -0.108 )
Explanation: -0.108 is greater because it is closer to zero than -0.18. Writing -0.18 as -0.180 makes the comparison clear: -0.108 > -0.180. Option A is smaller, not greater. Exam tip: for negative decimals, the number with the smaller absolute value is greater.
Correct answer: A. 6
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-4+16}{2}=\frac{12}{2}=6\). Therefore, 6 is correct. Neither 5 nor 7 is at an equal distance from -4 and 16. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: A. \(\sqrt{5}\)
Explanation: Since 5 is not a perfect square, \(\sqrt{5}\) is irrational and cannot be written as \(p/q\). Steps of \(1/n\) reach only rational points of the form \(k/n\). Exam tip: terminating and repeating decimals are rational.
Correct answer: A. 14
Explanation: On a number line, the distance between two numbers is the absolute value of their difference. Thus, \(|-13-(-27)|=|-13+27|=|14|=14\). Therefore, 14 is correct. The value 13 is only the absolute value of one number, not the distance between the two numbers. Exam tip: A distance is always non-negative.
Correct answer: A. -6
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-2+(-10)}{2}=\frac{-12}{2}=-6\). Therefore, \(-6\) is correct. \(-5\) is not the midpoint because it is not equally distant from \(-2\) and \(-10\). Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: A. Point A lies to the left of B.
Explanation: Since \(\sqrt{7}\approx2.646\), we get \(-\sqrt{7}\approx-2.646\). As \(-2.646<-2.6\), A is to the left of B. Exam tip: among negative numbers, the value with greater magnitude lies further left.
