Number line

\(\frac{9}{10}=0.9\), so it is greater than 0 and less than 1. Therefore, it lies between 0 and 1 on the number line. Option B is incorrect because \(\frac{9}{10}\) is less than 1. Exam tip: compare the fraction with 0 and 1 first to locate it quickly.

To lie strictly between 0 and 1, a number must be greater than 0 and less than 1. Convert the relevant fractions to decimals or compare numerator and denominator: 3/4 = 0.75, so 0 < 0.75 < 1. Therefore option C is correct. The value 7/5 = 1.4 is greater than 1, -1/2 = -0.5 is less than 0, and 2 is greater than 1. The real number line makes this comparison direct: numbers to the right of 0 but before 1 satisfy the condition. Only 3/4 occupies that interval among the given choices.

The governing concept is comparison of signed real numbers on the number line. On a number line, numbers increase from left to right; a number farther left is smaller, and a number farther right is greater. The point −3 lies to the left of −1, and −1 lies to the left of 2. Hence the increasing order is −3 < −1 < 2, making option A correct. Option B reverses the natural order and places the positive number first. Option C incorrectly claims that −1 is less than −3, although −1 is actually greater than −3. Option D also begins with 2, so it is not an increasing sequence. Comparing positions on the number line is more reliable than judging only the visual size of negative numerals.

The square root of a number is the value whose square equals that number. Since \(0^2=0\), we have \(\sqrt{0}=0\). Therefore, it lies at the origin, or 0, on the number line. Choosing 1 confuses it with \(\sqrt{1}=1\); in an exam, first evaluate the square root.

−0.6 is negative, so it lies to the left of 0. Its absolute value is less than 1, so it lies to the right of −1. Therefore, −0.6 is between −1 and 0. Option A may seem close, but it represents an interval of positive numbers. Exam tip: Check the position by writing −1 < −0.6 < 0.

To locate −1.25, compare it with the neighboring integers −2 and −1. On the number line, −2 < −1.25 < −1 because −1.25 is 0.75 units to the right of −2 and 0.25 units to the left of −1. Therefore it lies between −2 and −1, so option D is correct. The negative sign places the number to the left of zero, and the magnitude greater than 1 places it beyond −1. Option B would contain numbers such as −0.5, which are greater than −1; options A and C are positive intervals and cannot contain a negative number.

On a number line, the number farther to the right is greater. Since 7 lies to the right of 3, 7 is the greater number. Choosing 3 is incorrect because it lies to the left of 7. Exam tip: when comparing numbers on a number line, select the one farther to the right.

On the number line, 0 represents the origin. It lies to the right of negative numbers and to the left of positive numbers; therefore, calling it the origin is more precise than calling it the geometric ‘center’ of the number line. Exam tip: negative numbers are written to the left of 0 and positive numbers to its right.

On the number line, numbers smaller than 5 lie to the left of 5. Among the given options, 4 is one less than 5, so it is the correct answer. The numbers 6, 7, and 8 are greater than 5. Exam tip: Numbers increase when moving right on the number line and decrease when moving left.

Every rational number, such as \(\frac{1}{2}\), \(-\frac{3}{4}\), or \(2\), is represented by exactly one fixed point on the number line. Option C is incorrect because there are infinitely many rational numbers between any two rational numbers. Exam tip: Numbers to the right on a number line are greater, while numbers to the left are smaller.

On a number line, numbers to the left of zero are negative. −3 is less than zero, so it is a negative number. In contrast, 2, 4, and 5 lie to the right of zero and are positive numbers. In an exam, identify a negative number by the minus sign (−) before it.

On a number line, the value of numbers increases as we move from left to right. Therefore, a number to the left is smaller than a number to the right. Option B states the reverse and is incorrect. Negative numbers lie to the left of 0, and 0 has a fixed position on the number line. Exam tip: Remember: right means greater and left means smaller.

Positive numbers are greater than zero and lie to the right of zero on the number line. Among the given options, 3 is greater than zero, so it is the correct answer. −4 and −1 are negative, while 0 is neither positive nor negative. Exam tip: to check whether a number is positive, determine whether it is greater than 0.

The midpoint of two numbers is their average: \((1+9)÷2=10÷2=5\). Therefore, 5 is correct. Choosing 4 or 6 would not place the point at equal distances from both numbers. In an exam, add the two endpoints and divide the sum by 2 to find the midpoint.

On a number line, numbers to the right of 0 are greater than 0. Among the given options, 3 lies to the right of 0, so it is the correct answer. −1, −2, and −5 lie to the left of 0 and are less than 0. Exam tip: every positive number is greater than 0.

8 is a positive number. On a number line, positive numbers are located to the right of zero, so 8 lies to the right of zero. Negative numbers lie to the left of zero. Exam tip: identify the sign of a number first—positive numbers are placed to the right and negative numbers to the left.

On the number line, the negative number closer to zero is greater. Since −3 is closer to zero than −7, we have −3 > −7. Exam tip: among negative numbers, the one with the smaller absolute value is greater.

On the number line, there are 4 units from 0 to 4. Distance is found using the absolute difference: \(|4-0|=4\). Therefore, the correct answer is 4. Remember that distance is always non-negative, so reversing the order still gives 4.

On a number line, negative numbers are placed to the left of 0. Therefore, minus2 is located two units to the left of 0. Moving to the right of 0 gives positive numbers, so “To the right” is incorrect. Exam tip: place every negative number to the left of zero.

On the number line, 0 lies to the left of 1, so 0 is smaller than 1. The numbers 2, 3, and 5 lie to the right of 1 and are greater than 1. For exams, remember that the number farther to the left on a number line is smaller.