Number line

The absolute value of -9 is 9, whereas the absolute value of 6 is 6. Since 9 > 6, -9 has the greater absolute value. As 6 is positive, its absolute value remains 6. Exam tip: absolute value is the distance from 0 on the number line, so it is never negative.

In increasing order, numbers are arranged from smallest to greatest. On the number line, -7 lies to the left of -3, and -3 lies to the left of 2. Therefore, the correct order is -7, -3, 2. In option A, -3 is placed before -7, which is incorrect. Exam tip: Among negative numbers, the number with the greater absolute value is smaller.

The distance between two numbers on a number line is their absolute difference: \(|-4-(-10)|=|6|=6\). Therefore, the correct answer is 6. The value 14 comes from adding the magnitudes of the two numbers, not from their distance. Exam tip: always use \(|a-b|\) to find distance on a number line.

\(\sqrt{2}\) is irrational but real, so it has a definite point on the number line. Since \(1^2<2<2^2\), it lies between 1 and 2. Exam tip: irrational does not mean non-real.

On a number line, moving left means subtracting. Therefore, moving 3 steps left from 2 gives \(2-3=-1\). The number 0 would be reached by moving only 2 steps left from 2. Exam tip: add when moving right and subtract when moving left.

On a number line, the number farther to the right is greater. Since 0 lies to the right of -1, -3, and -6, it is the greatest number. Although -1 is the greatest negative number here, it is still less than 0. Exam tip: Among negative numbers, the number closer to zero is greater.

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.