Number line

( 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.