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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.
The midpoint of two numbers is their average: \(\frac{-3+9}{2}=\frac{6}{2}=3\). Therefore, the correct answer is 3. Note that 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 on a number line.
For negative numbers, the number closer to zero is greater. Since \(-0.09\) is closer to zero than \(-0.9\), we have \(-0.09 > -0.9\). The options \(0.09\) and \(0.9\) are positive numbers, so they are not the numbers being compared. Exam tip: among negative decimals, the one with the smaller absolute value is greater.
-2.4 can be written as -2.40. Since -2.40 is more negative than -2.04, it lies farther to the left on the number line and is therefore smaller. Option -2.04 is negative, but it is greater than -2.4. Exam tip: Add trailing zeros when needed to compare decimal places easily.
Moving to the right means adding the distance, so \(P=-1+\sqrt{13}\). As \(3.6<\sqrt{13}<3.7\), we get \(2.6<P<2.7\). Therefore, \(P\) lies between 2 and 3; do not treat the starting coordinate as zero.
The midpoint of two numbers on a number line is their average: \(\frac{-4+18}{2}=\frac{14}{2}=7\). Therefore, the correct answer is 7. A value such as 6 may result from an incorrect calculation of the sum or division. Exam tip: Include the signs of both numbers, add them, and then divide by 2.
The midpoint of two numbers on a number line is their average: \(\frac{-1+7}{2}=\frac{6}{2}=3\). Therefore, 3 is correct. Option 2 is not correct because it is not equally distant from -1 and 7. Exam tip: Add the two numbers and divide by 2 to find the midpoint.
-3.5 can be written as -3.50. On the number line, the more negative number lies farther to the left and is smaller. Therefore, -3.50 is smaller than -3.05. The options 3.05 and 3.5 are positive, so both are greater than either negative number. Exam tip: When comparing negative decimals, add zeros if needed to make the decimal places equal.
The midpoint of two numbers on a number line is their average: \(\frac{-9+15}{2}=\frac{6}{2}=3\). Hence, 3 is correct. \(-3\) is not at an equal distance from both numbers. Exam tip: add the two numbers and divide the result by 2 to find the midpoint.
The correct answer is -0.101. We can write -0.11 as -0.110. On comparing them, -0.101 is greater than -0.110 because, among negative numbers, the number closer to zero is greater. The two numbers are not equal. Exam tip: While comparing negative decimals, add trailing zeros to make the number of decimal places equal.
The midpoint of two numbers on a number line is their average: \(\frac{-2+22}{2}=\frac{20}{2}=10\). Therefore, 10 is correct. 11 is not correct because it is not equally distant from −2 and 22. 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: \(\lvert -40-(-20)\rvert=\lvert -20\rvert=20\). Therefore, the correct answer is 20. \(-20\) is the signed difference, not a distance, because distance cannot be negative. Exam tip: Always use the absolute value of the difference when finding distance.
\(-0.004\) is greater than \(-0.04\) because, among negative numbers, the number closer to zero is greater. On the number line, \(-0.004\) lies to the right of \(-0.04\). \(0.004\) and \(0.04\) are positive numbers, so they do not answer the comparison between the two given numbers. Exam tip: When comparing negative decimals, identify which number is closer to zero.
The midpoint of two numbers on a number line is their average: \(\frac{-8+4}{2}=\frac{-4}{2}=-2\). Hence, \( -2 \) is correct. \( -4 \) is not equally distant from \( -8 \) and \( 4 \), so it is not the midpoint. Exam tip: add the two numbers and divide the result by 2 to find their midpoint.
Write the numbers to the same number of decimal places: -0.62 = -0.620. Now compare them: -0.602 is greater than -0.620 because, among negative numbers, the number closer to zero is greater. The positive numbers 0.602 and 0.620 are not valid answers for comparing the given negative numbers. Exam tip: Add trailing zeros when needed to make the decimal places equal before comparing decimals.
The midpoint of two numbers on a number line is their average: \(\frac{-11+(-19)}{2}=\frac{-30}{2}=-15\). Therefore, \(-15\) is correct. \(-14\) is not the midpoint because it is 3 units from \(-11\) and 5 units from \(-19\). Exam tip: add the numbers with their signs, then divide by 2.
The midpoint of two numbers on a number line is their average: \(\frac{-3+21}{2}=\frac{18}{2}=9\). Therefore, 9 is correct. Neither 8 nor 10 is at an equal distance from both numbers. Exam tip: Add the two numbers and divide the result by 2 to find their midpoint.
Since \(2<\left(\frac{3}{2}\right)^2=\frac94<3\), we get \(\sqrt2<\frac32<\sqrt3\). Thus \(\frac32\) is a rational number between them; in fact, infinitely many rationals lie between distinct real numbers. Exam tip: compare positive roots by squaring.
\(\sqrt{2}\) is irrational, and \(1.4^2=1.96<2<2.25=1.5^2\), so \(1.4<\sqrt{2}<1.5\). Thus, the interval contains an irrational number. Exam tip: compare squares of the endpoints to locate a square root.
The midpoint of two numbers on a number line is their average: \(\frac{-6+30}{2}=\frac{24}{2}=12\). Therefore, 12 is correct. For example, 18 is not at an equal distance from -6 and 30. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Write \(-0.77\) as \(-0.770\) to compare the decimals. Since \(-0.770 < -0.707\), \(-0.77\) is smaller. The closest distractor, \(-0.707\), is closer to zero and is therefore greater. Exam tip: among negative decimals, the number farther left on the number line is smaller.
The midpoint of two numbers is their average: \(\frac{-9+(-21)}{2}=\frac{-30}{2}=-15\). Therefore, \(-15\) is correct. A value such as \(-14\) is not at an equal distance from both numbers. Exam tip: when adding negative numbers, add their magnitudes and retain the negative sign.
The midpoint of two numbers on a number line is their average: \(\frac{-2+18}{2}=\frac{16}{2}=8\). Therefore, 8 is correct. The value 9 is not the average of -2 and 18. Exam tip: add the two numbers and divide by 2 to find their midpoint.
On a number line, the distance between two numbers is the absolute value of their difference: \(\lvert -35-(-15)\rvert=\lvert -20\rvert=20\). Therefore, the correct answer is 20. The option 18 comes from an incorrect subtraction. Exam tip: distance is always non-negative.
Write \(-0.51\) as \(-0.510\) to compare the decimals. Since \(-0.509\) is greater than \(-0.510\), \(-0.509\) is the correct answer. Among negative numbers, the number closer to zero is greater. Although \(-0.501\) would be greater than both given numbers, it is not one of the two numbers being compared. Exam tip: first make the number of decimal places equal before comparing decimals.
Between any \(a<b\), there are infinitely many rational as well as irrational numbers, so C is correct. In exams, remember that the real number line has no gaps between two real numbers.
QUIZ COMPLETE
