Verified Answer :

  • Convert the mixed number \(-2 \frac{1}{2}\) to the decimal \(-2.5\).
  • Recognize that \(-2.5\) lies exactly halfway between the integers \(-2\) and \(-3\).
  • Select the number line depiction where the point is positioned at the midpoint of the segment connecting \(-2\) and \(-3\).
  • The correct position is \(\boxed{-2.5}\).

Explanation

  1. Analyzing the Position of -2 1/2

To locate the number \(-2 \frac{1}{2}\) on a number line, we first express it as a decimal. Since \(\frac{1}{2} = 0.5\), we have \(-2 \frac{1}{2} = -2 - 0.5 = -2.5\). On the number line, negative numbers increase in magnitude as we move to the left, away from zero. Thus, \(-2.5\) is a value that is greater than \(-3\) and less than \(-2\). Specifically, it is located exactly at the midpoint between the integer marks \(-2\) and \(-3\).

  1. Identifying the Correct Representation

To identify the correct position on a number line, examine the interval between \(-2\) and \(-3\). A number line representation of \(-2.5\) should show a point or mark placed precisely halfway between the integer labels \(-2\) and \(-3\). If an image has a mark shifted closer to either \(-2\) or \(-3\), it would not correctly represent \(-2.5\). Therefore, the correct visual representation is the one where the point is exactly equidistant from the marks for \(-2\) and \(-3\).

Examples

Understanding how to locate fractions and decimals on a number line is essential for navigation and measurement. For instance, if you are reading a thermometer that marks temperatures in degrees, seeing a value like \(-2.5^{\circ}\text{C}\) means you must look exactly halfway between the mark for \(-2^{\circ}\text{C}\) and \(-3^{\circ}\text{C}\). Mastering these placements allows for precise readings on scales like speedometers, rulers, and gauges, ensuring accuracy in everyday measurements.

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