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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.
TOPIC PRACTICE
Up to 25 questions from this page. Select your focus, then start.
For negative numbers, the number farther to the right on the number line is greater. \(-20.5\) lies to the right of \(-21\) because it is closer to zero. Therefore, \(-20.5\) is greater. Although \(-20.75\) is also greater than \(-21\), it is not one of the two numbers being compared. Exam tip: among negative numbers, the number with the greater negative value is smaller.
For negative numbers, the number closer to zero is greater. \(-0.007\) is closer to zero than \(-0.07\), so \(-0.007 > -0.07\). Choosing \(-0.07\) is a common error because, among negative numbers, the one with the larger magnitude is smaller. Exam tip: write \(-0.07\) as \(-0.070\) before comparing decimal places.
Between any two distinct real numbers, there are infinitely many rational and infinitely many irrational numbers. Hence every non-zero interval on the number line contains both types. Exam tip: when you see “two distinct real numbers,” recall the density property.
The midpoint of two numbers on a number line is their average: \(\frac{-10+6}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is correct. \(2\) may result from ignoring the negative sign, but the sum of \(-10\) and \(6\) is \(-4\). Exam tip: first add both numbers carefully, then divide the result by 2.
The distance between two numbers on a number line is the absolute value of their difference. Thus, \(|4-(-17)|=|21|=21\). Therefore, 21 is correct. Choosing 20 would result from missing the sign change when subtracting a negative number. Exam tip: always take the absolute value of the difference when finding distance.
The successor of an integer is obtained by adding 1. Thus, \(-31+1=-30\), so -30 is the correct answer. -32 is the predecessor of -31 because it lies one step to the left of -31 on the number line. Exam tip: moving one step right on a number line increases the number by 1.
The predecessor of a whole number is exactly 1 less than that number. Therefore, the predecessor of 20 is \(20-1=19\). Since 18 is 2 less than 20, it is not the predecessor. Exam tip: subtract 1 from the given number to find its predecessor.
The absolute value of a number is its distance from 0 on the number line. Since \(-19\) is 19 units away from 0, \(|-19|=19\). \(-19\) is the number itself, not its absolute value. Exam tip: the absolute value of a negative number is always positive.
Real numbers are dense on the number line. For example, between 1 and 2, \(3/2\) is rational while \(\sqrt{2}\) is irrational, and infinitely many more exist. Exam tip: unlike integers, real numbers have no consecutive pair.
The midpoint of two numbers on a number line is their average: \(\frac{-7+(-1)}{2}=\frac{-8}{2}=-4\). Therefore, \((-4)\) is the correct answer. \((-5)\) is closer to one of the numbers and is not equally distant from both. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Write \(-2.5\) as \(-2.50\) to compare the decimals. Since \(-2.05\) is closer to zero and lies to the right of \(-2.50\) on the number line, \(-2.05\) is greater. Choosing \(-2.5\) is incorrect because, among negative numbers, the number with the larger magnitude is smaller. Exam tip: Add trailing zeros when needed before comparing decimals.
On the number line, the number to the right is greater.
( -0.0009 ) is a negative number and lies to the left of 0, so 0 is greater. “Both are equal” is incorrect because one number is zero and the other is negative. Exam tip: Zero is always greater than any negative number.
The distance between two numbers on a number line is the absolute value of their difference. Here, \(\lvert -5-(-12)\rvert=\lvert 7\rvert=7\), so 7 is correct. Getting 8 would result from an incorrect subtraction. Exam tip: a distance is always non-negative.
Between any two distinct rational numbers, there are infinitely many rational as well as irrational numbers. Hence C is correct; B is false because irrationals also occur between them. Exam tip: real numbers are dense on the number line.
\(0\) is greater than \(-6\) and less than \(1\), so it lies between the two numbers. \(-7\) and \(-8\) are less than \(-6\), while \(2\) is greater than \(1\). Exam tip: To check whether a number lies between two values, verify that it is greater than the left value and less than the right value.
On a number line, the midpoint of 3 and 11 is their average: \(\frac{3+11}{2}=\frac{14}{2}=7\). Therefore, 7 is correct. The number 6 is not at an equal distance from 3 and 11. Exam tip: To find the midpoint of two numbers, add them and divide by 2.
(1.1) can be written as 1.10. Comparing 1.10 and 1.01, the tenths digit is 1 in 1.10 but 0 in 1.01. Therefore, (1.1) is greater. (1.01) is smaller, and the two numbers are not equal. Exam tip: When comparing decimals, add zeros at the end if needed so that corresponding place values can be compared.
Since \(1^2=1\) and \(2^2=4\), \(\sqrt{2}\) lies between 1 and 2. As 2 is not a perfect square, \(\sqrt{2}\) is irrational, not a midpoint or an integer. Exam tip: compare neighbouring squares to locate roots.
On a number line, the distance between two numbers is the absolute value of their difference: \(\left|-8-(-2)\right|=\left|-6\right|=6\). Therefore, the correct answer is 6. The value 8 is only the magnitude of \(-8\), not the distance between the two numbers. Exam tip: a distance is always non-negative.
\( -14.9 \) is greater than \( -15 \) because it lies to the right of \( -15 \) on the number line and is closer to zero. Among negative numbers, the number closer to zero is greater. Thus, \( -15 \) is smaller, and the two numbers are not equal. Exam tip: when comparing negative numbers, the number farther right on the number line is greater.
The midpoint of two numbers on a number line is their average: \(\frac{-9+3}{2}=\frac{-6}{2}=-3\). Therefore, \(-3\) is correct. \(-6\) is the sum of the two numbers, not their midpoint. Exam tip: add the two numbers and divide by 2 to find their midpoint.
The successor of an integer is found by adding 1 to it. Thus, 99 + 1 = 100, so 100 is the correct answer. 101 is the second integer after 99, not its immediate successor. Exam tip: always add 1 to find a successor.
The predecessor of a number is 1 less than the number. Hence, \(-50-1=-51\). \(-49\) is the successor because it is 1 greater than \(-50\). Exam tip: subtract 1 to find a predecessor.
The absolute value of a number is its distance from 0 on the number line, so it cannot be negative. Hence,
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In increasing order, numbers are written from smallest to largest. Among negative numbers, the number farther to the left of zero is smaller. Thus, -4 < -2 < -1 < 3, so the correct order is ( -4, -2, -1, 3 ). In option B, -1 is placed before -2, which is incorrect. Exam tip: On a number line, the number to the left is always smaller.
QUIZ COMPLETE
