Question

49 the goal of a video game is to find hidden gems on a number line. 49 an emerald is hidden at point e. which number describes the location of the emerald? $3$, $3\frac{1}{2}$, $4$, $4\frac{1}{2}$

Explanation:

Step1: Analyze the number line

The number line has marks at \( 0, \frac{1}{2}, 1, 1\frac{1}{2}, 2, 2\frac{1}{2}, 3, 4, 5 \). The distance between consecutive marks (like from \( 3 \) to \( 4 \)) is \( 1 \), and it's divided into two equal parts (since there's a mark at \( 3\frac{1}{2} \) between \( 3 \) and \( 4 \)).

Step2: Locate point E

Point E is between \( 3 \) and \( 4 \), and it's at the mid - point of the interval from \( 3 \) to \( 4 \). The mid - point of the interval \([3,4]\) is calculated as \( 3+\frac{4 - 3}{2}=3+\frac{1}{2}=3\frac{1}{2}\). So the number that describes the location of the emerald at point E is \( 3\frac{1}{2} \).

Answer:

\( 3\frac{1}{2} \)