Representing real numbers on the number line

(5) is positive, so it lies (5) units to the right of (0). In exams, remember right direction for positive numbers.

(-6) is negative, so it lies (6) units to the left of (0). In exams, choose the left direction for negative numbers.

(\frac{2}{5}) is greater than (0) and less than (1). In exams, place a proper fraction between (0) and (1).

(-\frac{3}{4}) is negative and greater than (-1). In exams, show such fractions between (-1) and (0).

(1.25) is greater than (1) and less than (2). In exams, compare a decimal with nearby integers.

(-2.5) is greater than (-3) and less than (-2). In exams, be careful because order with negative decimals can feel reversed.

(0) is treated as the origin of the number line. In exams, place positive numbers to the right and negative numbers to the left.

(\frac{1}{3}) has the smallest distance from (0). In exams, check distance for closeness and not only the sign.

The distance is (10-7=3) units. In exams, subtract the smaller number from the larger number to find distance.

The distance between two numbers is the absolute value of their difference: |−1 − (−5)| = |4| = 4 units. Therefore, option C is correct. Choosing 6 units incorrectly adds the magnitudes directly instead of finding the difference between the positions. In an exam, remember that distance is always positive.

The midpoint of two numbers is their average: \(\frac{2+6}{2}=\frac{8}{2}=4\). Therefore, 4 is correct. The numbers 3 and 5 are not equidistant from both given points, while 8 does not lie between them. In an exam, use the midpoint formula \(\frac{x_1+x_2}{2}\).

(\sqrt{9}=3), so its position is at (3). In exams, identify square roots of perfect squares quickly.

(\sqrt{16}=4), so (-\sqrt{16}=-4). In exams, apply the outside negative sign after finding the square root.

Since (4^2=16) and (5^2=25), (\sqrt{20}) lies between (4) and (5). In exams, find nearby perfect squares.

Since (\sqrt{7}) lies between (2) and (3), (-\sqrt{7}) lies between (-3) and (-2). In exams, note the direction of a negative square root.

(\frac{7}{2}=3.5), so it lies between (3) and (4). In exams, convert an improper fraction into a decimal or mixed number.

(-\frac{9}{2}=-4.5), so it lies between (-5) and (-4). In exams, place a negative mixed number in the correct interval.

(1+\frac{2}{5}=1.4), so it is two parts after (1). In exams, take each equal part as (\frac{1}{5}).

Since \(0.6\) has one digit after the decimal point, it can be written as \(\frac{6}{10}\). Reducing numerator and denominator by 2 gives \(\frac{3}{5}\), so option A is correct. Options B, C and D represent approximately 1.67, 6 and 0.167 respectively. Exam tip: use 10, 100 or 1000 as the denominator according to the number of decimal places, then simplify the fraction.

(\sqrt{10}) is greater than (3) because (3^2=9) and (10) is larger. In exams, check square root positions using squares.