Number line

\(0\) is greater than \(-6\) and less than \(1\), so it lies between the two numbers. \(-7\) and \(-8\) are less than \(-6\), while \(2\) is greater than \(1\). Exam tip: To check whether a number lies between two values, verify that it is greater than the left value and less than the right value.

On a number line, the midpoint of 3 and 11 is their average: \(\frac{3+11}{2}=\frac{14}{2}=7\). Therefore, 7 is correct. The number 6 is not at an equal distance from 3 and 11. Exam tip: To find the midpoint of two numbers, add them and divide by 2.

(1.1) can be written as 1.10. Comparing 1.10 and 1.01, the tenths digit is 1 in 1.10 but 0 in 1.01. Therefore, (1.1) is greater. (1.01) is smaller, and the two numbers are not equal. Exam tip: When comparing decimals, add zeros at the end if needed so that corresponding place values can be compared.

Since \(1^2=1\) and \(2^2=4\), \(\sqrt{2}\) lies between 1 and 2. As 2 is not a perfect square, \(\sqrt{2}\) is irrational, not a midpoint or an integer. Exam tip: compare neighbouring squares to locate roots.

On a number line, the distance between two numbers is the absolute value of their difference: \(\left|-8-(-2)\right|=\left|-6\right|=6\). Therefore, the correct answer is 6. The value 8 is only the magnitude of \(-8\), not the distance between the two numbers. Exam tip: a distance is always non-negative.

\( -14.9 \) is greater than \( -15 \) because it lies to the right of \( -15 \) on the number line and is closer to zero. Among negative numbers, the number closer to zero is greater. Thus, \( -15 \) is smaller, and the two numbers are not equal. Exam tip: when comparing negative numbers, the number farther right on the number line is greater.

The midpoint of two numbers on a number line is their average: \(\frac{-9+3}{2}=\frac{-6}{2}=-3\). Therefore, \(-3\) is correct. \(-6\) is the sum of the two numbers, not their midpoint. Exam tip: add the two numbers and divide by 2 to find their midpoint.

The successor of an integer is found by adding 1 to it. Thus, 99 + 1 = 100, so 100 is the correct answer. 101 is the second integer after 99, not its immediate successor. Exam tip: always add 1 to find a successor.

The predecessor of a number is 1 less than the number. Hence, \(-50-1=-51\). \(-49\) is the successor because it is 1 greater than \(-50\). Exam tip: subtract 1 to find a predecessor.

The absolute value of a number is its distance from 0 on the number line, so it cannot be negative. Hence,

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In increasing order, numbers are written from smallest to largest. Among negative numbers, the number farther to the left of zero is smaller. Thus, -4 < -2 < -1 < 3, so the correct order is ( -4, -2, -1, 3 ). In option B, -1 is placed before -2, which is incorrect. Exam tip: On a number line, the number to the left is always smaller.

Real numbers are dense on the number line: between any two distinct real numbers, infinitely many rational and irrational numbers exist. Exam tip:
\(\sqrt{2}\) also corresponds to one definite point on the number line.

\( -6.6 = -6.60 \) because a zero added at the end of a decimal does not change its value. Hence, both numbers represent the same point on the number line. Choosing \( -6.6 \) as greater is incorrect; the extra zero only shows an additional decimal place. Exam tip: Remove trailing zeros before comparing decimals.

The midpoint of two numbers \(a\) and \(b\) is \(\frac{a+b}{2}\). Therefore, \(\frac{-20+(-4)}{2}=\frac{-24}{2}=-12\). Hence, \(-12\) is the correct answer. \(-10\) would be the midpoint of \(-20\) and \(0\), so it is not correct here. Exam tip: When adding negative numbers, add their magnitudes and keep the negative sign.

On a number line, the distance between two numbers is the absolute value of their difference: \(|9-(-3)|=|12|=12\). Therefore, the correct answer is 12. Although -12 can be a difference depending on the order of subtraction, distance is never negative. Exam tip: always take the absolute value of the difference in distance questions.

The integers strictly between ( -8 ) and ( -1 ) are ( -7 ), ( -6 ), ( -5 ), ( -4 ), ( -3 ), and ( -2 ). Therefore, ( -7 ) is correct. ( -9 ) lies to the left of ( -8 ) on the number line, while ( 0 ) and ( -1 ) are not inside the interval; ( -1 ) is an endpoint. Exam tip: “Between” usually excludes the two given endpoints.

0.005 is greater. In 0.005, the digit 5 is in the thousandths place, whereas in 0.0005 it is in the ten-thousandths place. Writing them as 0.0050 and 0.0005 shows that 50 ten-thousandths is greater than 5 ten-thousandths. Exam tip: Add zeros to the right of decimals to make the number of decimal places equal before comparing.

0 is greater than -11 because on the number line, 0 lies to the right of -11. A number to the right on a number line is always greater. “Both are equal” is incorrect because -11 and 0 are different numbers. Exam tip: Every negative number is less than 0.

The midpoint of two numbers on a number line is their average: \(\frac{5+(-11)}{2}=\frac{-6}{2}=-3\). Therefore, \(-3\) is correct. \(-2\) is not correct because it is not equally distant from 5 and \(-11\). Exam tip: add the two numbers and divide the sum by 2 to find the midpoint.

The distance between two numbers on a number line is the absolute value of their difference. Thus, the distance is \(|8-(-6)|=|14|=14\). Therefore, 14 is correct. A value such as 12 can result from handling the negative sign incorrectly. Exam tip: always use the absolute value for distance, so the answer cannot be negative.