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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.
On a number line, the number farther to the right is greater. Since -2 lies to the right of -9 and is closer to zero, -2 is greater. The number -9 is smaller because it lies farther to the left. Exam tip: Among negative numbers, the number closer to zero is greater.
The successor of an integer is obtained by adding 1. Thus, \(-8+1=-7\), so -7 is correct. -9 is the predecessor of -8 because it lies one step to the left of -8 on the number line. Exam tip: Even for negative integers, moving right on the number line increases the number by 1.
The predecessor of a number is exactly one less than the number. Therefore, the predecessor of 5 is 5 - 1 = 4. The number 6 is the successor of 5 because it is one more than 5. Exam tip: subtract 1 to find a predecessor and add 1 to find a successor.
The midpoint of two numbers is their average: \(\frac{-6+4}{2}=\frac{-2}{2}=-1\). Therefore, \(-1\) is correct. Although \(0\) lies between the two numbers, it is not equally distant from -6 and 4. Exam tip: add the two numbers and divide by 2 to find their midpoint.
The distance between two numbers on a number line is the absolute value of their difference: \(|7-(-3)|=|10|=10\). Hence, the correct answer is 10.
-10 may arise from subtracting in the reverse order, but distance can never be negative. Exam tip: always take the absolute value of the difference when finding distance.
The correct answer is 0 because \(-\frac{1}{2}<0<\frac{1}{2}\). On the number line, 0 is to the right of \(-\frac{1}{2}\) and to the left of \(\frac{1}{2}\). The numbers \(-1\), 1, and 2 lie outside the given interval. Exam tip: Check whether a number lies between two values by writing it in an inequality chain.
Write 0.3 as 0.30. The numbers are then 0.30, 0.03, and 0.13. Comparing the first digits after the decimal point, 0.03 has 0, which is less than 1 in 0.13 and 3 in 0.30. Hence, 0.03 is the smallest. Although 0.13 is less than 0.30, it is greater than 0.03. Exam tip: Add zeros to the right of decimals when needed to compare place values easily.
The absolute value of a number is its distance from 0 on the number line. Since -5 is 5 units away from 0, \(|-5|=5\). Option -5 is the number itself, not its absolute value. Exam tip: An absolute value is never negative.
Since \(2^2=4\) and \(3^2=9\), the number 5 lies between 4 and 9. Therefore, \(\sqrt{5}\) lies between 2 and 3. In contrast, \(\sqrt{3}<2\) and \(\sqrt{10}>3\). Exam tip: compare nearby perfect squares to locate square roots.
On a number line, adding a positive number means moving that many units to the right. For example, to add 3 to 2, move 3 steps right from 2 to reach 5. Moving left represents subtraction or adding a negative number. Exam tip: while adding, count the required steps to the right for a positive addend.
On a number line, subtracting a positive number means moving to the left because the value decreases. For example, to find 5 - 2 = 3, move two steps left from 5. Moving to the right represents addition. Exam tip: in subtraction, count leftward from the starting number by the number being subtracted.
\(\frac{5}{2}=2.5\), and \(2<2.5<3\). Therefore, \(\frac{5}{2}\) is the rational number between 2 and 3. \(\frac{7}{2}=3.5\) is greater than 3, while \(\frac{3}{2}=1.5\) is less than 2. Exam tip: Convert a fraction to a decimal, or compare it using inequalities, to check whether it lies between two integers.
Since \(2^2=4\) and \(3^2=9\), \(4<5<9\) gives \(2<\sqrt{5}<3\). Also, \(\sqrt{5}\approx2.24\), so it is closer to 2, not 2.5. Exam tip: compare with nearby perfect squares first.
\(\frac{1}{3}=0.333\ldots\), whereas \(0.25=\frac{1}{4}\). Since \(0.333\ldots > 0.25\), \(\frac{1}{3}\) is greater. The “both are equal” option is incorrect because their decimal values are different. Exam tip: compare fractions by converting them to decimals or by using a common denominator.
The distance between two numbers on a number line is the absolute value of their difference. Thus, \(|0-(-10)|=|10|=10\) units. -10 shows a position or direction, not a distance. Exam tip: a distance is always zero or positive.
The midpoint of two numbers on a number line is their average: \(\frac{1+5}{2}=\frac{6}{2}=3\). Therefore, 3 is equally distant from 1 and 5. Option 2 is not the midpoint because it is 1 unit from 1 but 3 units from 5. Exam tip: add the two numbers and divide by 2 to find their midpoint.
In increasing order, numbers are written from smallest to greatest. On the number line, \(-2\) lies to the left of \(-1\), and \(3\) lies farthest to the right. Therefore, the correct order is \(-2, -1, 3\). In option C, \(-1\) is placed before \(-2\), which is incorrect. Exam tip: among negative numbers, the number with the greater negative value is smaller.
On a number line, the number to the right is greater. Since 0 lies to the right of -0.5, 0 is greater. -0.5 is a negative number, and every negative number is less than zero. Exam tip: Among negative numbers, the number closer to zero is greater.
The successor of an integer is obtained by adding 1. Thus, \(-1+1=0\), so 0 is the correct answer. \(-2\) is the predecessor of \(-1\), not its successor. Exam tip: on a number line, moving one step to the right increases the integer by 1.
On the number line, a number between -3 and 2 must be to the right of -3 and to the left of 2. Since
-3 < 0 < 2, 0 is the correct answer. -4 and -5 lie to the left of -3, while 3 lies to the right of 2. Exam tip: For a “between” question, compare the number with both endpoints.
On a number line, the reflection of a number about zero is its additive inverse. Since -6 is 6 units to the left of zero, its reflection is 6 units to the right of zero, i.e., 6. The option -6 is the original number, not its reflection. Exam tip: for reflection about zero, change the sign of the number.
The absolute value of a number is its distance from 0 on the number line. Since 0 is zero units away from itself, its absolute value is 0. The number 1 is one unit away from 0, so it is not correct. Exam tip: An absolute value is never negative.
On a number line, values increase as we move to the right.
-1 is greater than -2, so it lies to the right of -2. In contrast, -3 is less than -2 and lies to its left. Exam tip: Among negative numbers, the number closer to zero is greater.
On a number line, the number farther to the left is smaller. Among the given options, \(-2\) lies to the left of \(-1\), so \(-2\) is the smallest number. Both \(0\) and \(1\) are greater than negative numbers. Exam tip: among negative numbers, the one with the greater magnitude is smaller.
The distance between two numbers on a number line is the absolute value of their difference: \(|4-(-2)|=|6|=6\). Therefore, the correct answer is 6. The value 4 is the magnitude of one number, not the distance between the two numbers. Exam tip: always take the absolute value of the difference because distance cannot be negative.
QUIZ COMPLETE
