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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 to the right is greater. \( -3 \) lies to the right of \( -7 \) and is closer to zero, so \( -3 \) is greater. \( -7 \) is smaller because it lies further 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 to it. Thus, 6 + 1 = 7, so 7 is the correct answer. The number 6 is the given integer itself, not its successor. Exam tip: on a number line, the successor is the integer immediately to the right.
The predecessor of a number is exactly 1 less than the number. Thus, \(-4-1=-5\), so the correct answer is \(-5\). The number \(-3\) is the successor of \(-4\) because it is 1 greater. Exam tip: subtract 1 for a predecessor and add 1 for a successor.
The distance between two numbers on a number line is the absolute value of their difference: \(|3-(-8)|=|11|=11\). Therefore, 11 is correct. \(-11\) may arise as a signed difference, but distance can never be negative. Exam tip: always take the absolute value when finding distance.
( 0 ) is greater than ( -1 ) and smaller than ( 2 ), i.e., \( -1 < 0 < 2 \). Therefore, it lies between the two numbers. ( -2 ) and ( 3 ) are outside the given interval. Exam tip: To check whether a number lies between two numbers, compare it with the smaller and larger numbers.
0.4 can be written as 0.40. Comparing 0.40 and 0.04, 40 hundredths is greater than 4 hundredths, so 0.4 is greater. The close distractor 0.04 is smaller because it represents only 4 hundredths. Exam tip: Add zeros to the right of a decimal, if needed, to make the number of decimal places equal before comparing.
The absolute value of a number is its distance from zero on the number line. Since \(-9\) is 9 units away from zero, \(|-9|=9\). \(-9\) is the original number, not its absolute value. Exam tip: the negative sign is removed when finding the absolute value of a negative number.
On a number line, 0 is the origin. Negative numbers lie to its left and positive numbers lie to its right, so 0 lies between them. Saying “the centre” is not always precise because a number line extends infinitely in both directions. Exam tip: numbers increase as you move right and decrease as you move left.
On a number line, adding a positive number means moving to the right. Therefore, to add 3 to 5, move 3 units right from 5 and reach 8. Moving left represents subtraction or adding a negative number. Exam tip: remember: addition moves right, while subtraction moves left.
\(2-6=-4\). On the number line, start at 2 and move 6 steps to the left to reach \(-4\). \(4\) would be obtained by calculating \(6-2\), not \(2-6\). Exam tip: in subtraction, move left by the value being subtracted.
In decreasing order, numbers are arranged from greatest to smallest from left to right. In option B, 3 > 2 > 1, so it is the correct decreasing order. In option D, -3 < -2 < -1, so it is an increasing order. Exam tip: Among negative numbers, the number closer to zero is greater.
\( -\frac{3}{2}=-1.5 \) and \( -\frac{1}{2}=-0.5 \). On the number line, \( -1.5 \) lies to the left of \( -0.5 \), so \( -\frac{3}{2} \) is smaller. They are not equal because their values differ. Exam tip: among negative numbers, the number with the greater magnitude is smaller.
\(\frac{1}{5}=0.2\) because dividing 1 by 5 gives 0.2. Therefore, both numbers have the same value, so neither is greater. Choosing \(\frac{1}{5}\) or \(0.2\) as greater is incorrect because they are two forms of the same number. Exam tip: To compare a fraction with a decimal, convert the fraction into its decimal form.
(-0.6) can be written as -0.60. On the number line, -0.60 lies to the left of -0.06, so (-0.6) is smaller. (-0.06) is closer to zero and is therefore greater. Exam tip: Write negative decimals to the same number of decimal places before comparing them.
The midpoint of two numbers on a number line is their average. Thus, \(\frac{2+8}{2}=\frac{10}{2}=5\), so 5 is correct. Although 4 is closer to 2, it is not equally distant from 2 and 8; 5 is three units from each number. 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 positive value of their difference. Here, \(|5-(-1)|=|6|=6\). Therefore, 6 is correct. Choosing 5 can result from mishandling the subtraction of a negative number; subtracting \(-1\) means adding 1. Exam tip: always take the absolute value when finding distance on a number line.
Values increase as we move from left to right on a number line. Thus, since \(-2<3\), \(-2\) lies to the left of 3. Option B reverses this order. Exam tip: place the smaller number on the left when comparing points.
Since \(1^2=1\) and \(2^2=4\), with \(1<2<4\), we get \(1<\sqrt{2}<2\). An irrational number has a definite point on the number line; it is not unmarkable. Exam tip: compare nearby squares to locate a square root.
On a number line, numbers increase as we move to the right. The number immediately to the right of \(-2\) is \(-1\), so option B is correct. \(-3\) lies to the left of \(-2\) because it is smaller. Exam tip: Among negative numbers, the number closer to zero is greater.
On the number line, numbers to the right of -4 and to the left of 1 lie between them. Since 0 is greater than -4 and less than 1, it is the correct answer. In contrast, -5 is less than -4, so it is not in this interval. Exam tip: For “between,” check that the number lies between both endpoints.
Since \(1^2<2<2^2\), \(\sqrt{2}\) lies between 1 and 2 on the number line. It is irrational, so its decimal expansion is non-terminating and non-repeating. Exam tip: a repeating decimal is rational.
On a number line, the number farther to the right is greater. \(6\) lies to the right of \(-6\) and is positive, so \(6>-6\). “Both are equal” is incorrect because the two numbers have different values. Exam tip: Every positive number is greater than every negative number.
\(\frac{3}{2}=1.5\). Hence, \(1.2\) lies between \(1\) and \(\frac{3}{2}\), since \(1<1.2<1.5\). Option \(2\) may seem close, but it is greater than \(1.5\). Exam tip: convert fractions to decimals and compare their order on the number line.
1.0 is greater than 0.9 and less than 1.1; that is, \(0.9 < 1.0 < 1.1\). Therefore, 1.0 lies between the two numbers. 0.8 is less than 0.9, while 1.2 and 1.3 are greater than 1.1. Exam tip: To check whether a number lies between two values, compare it with both limits.
In increasing order, numbers are written from smallest to greatest. Here,
\, -3 < -2 < 1
, so the correct order is
( -3, -2, 1 )
. The sequence
( -2, -3, 1 )
is not increasing because -3 is smaller than -2. Exam tip: On a number line, the number farther to the left is smaller.
QUIZ COMPLETE
