Question

look at the number line below.
which point is located at $-dfrac{5}{8}$?
choose 1 answer:
a point a
b point b
c point c
d point d

Explanation:

Step1: Analyze the number line scale

First, we need to determine the value of each small tick on the number line. Let's assume the distance between -1 and 0 (or 0 and 1, -2 and -1) is divided into equal parts. Let's find the length of each interval. From -1 to 0, let's see how many ticks are there. Wait, actually, let's convert \(-\frac{5}{8}\) to a decimal to understand its position: \(-\frac{5}{8}=-0.625\). Now, let's analyze the positions of the points:

• Point A is at -2 (or close to -2, but \(-\frac{5}{8}\) is greater than -1? Wait no, \(-\frac{5}{8} = -0.625\), which is between -1 and 0? Wait no, -0.625 is between -1 and 0? Wait, -1 is -1.0, 0 is 0.0. So -0.625 is between -1 and 0? Wait no, -0.625 is greater than -1 (since -0.625 > -1) and less than 0. Wait, but let's check the number line:

Looking at the number line, between -1 and 0, how many ticks? Let's see, from -1 to 0, let's count the intervals. Wait, maybe the number line has each major tick (like -2, -1, 0, 1, 2) and between them, the number of small ticks. Let's see, between -1 and 0: let's see the position of point C. Wait, point C is between -1 and 0? Wait no, the number line: A is at -2, B is between -2 and -1, C is between -1 and 0, D is between 0 and 1.

Wait, \(-\frac{5}{8} = -0.625\), which is between -1 ( -1.0) and 0 (0.0), because -0.625 is greater than -1 and less than 0. So we can eliminate A (at -2) and B (between -2 and -1) and D (between 0 and 1). So only point C is between -1 and 0. Wait, but let's confirm the scale. Let's suppose that between -1 and 0, the number line is divided into 8 equal parts (since the fraction is eighths). So each part is \(\frac{1}{8}=0.125\). So starting from -1 (which is \(-\frac{8}{8}\)), moving towards 0, each tick is +\(\frac{1}{8}\). So:

• \(-\frac{8}{8}=-1\)

• \(-\frac{7}{8}=-0.875\)

• \(-\frac{6}{8}=-0.75\)

• \(-\frac{5}{8}=-0.625\)

• \(-\frac{4}{8}=-0.5\)

• etc.

So \(-\frac{5}{8}\) is the third tick from -1 towards 0? Wait, from -1 (-\(\frac{8}{8}\)):

1st tick: \(-\frac{7}{8}\)

2nd tick: \(-\frac{6}{8}\)

3rd tick: \(-\frac{5}{8}\)

So on the number line, between -1 and 0, the point at \(-\frac{5}{8}\) would be the third tick from -1 towards 0. Looking at the number line, point C is in that region. Let's check the options:

• Option A: Point A is at -2 (or near -2), so no.

• Option B: Point B is between -2 and -1, so no.

• Option C: Point C is between -1 and 0, which matches the position of \(-\frac{5}{8}\) (since -0.625 is between -1 and 0).

• Option D: Point D is between 0 and 1, so no.

Step2: Confirm the position

Since \(-\frac{5}{8} = -0.625\) is between -1 and 0, and among the points, only Point C is in that interval (between -1 and 0), while A is at -2, B is between -2 and -1, D is between 0 and 1. So the correct point is Point C.

Answer:

C. Point C