To determine which point represents [tex]\( -1 \frac{5}{8} \)[/tex] on the number line, let's convert the mixed number [tex]\( -1 \frac{5}{8} \)[/tex] into an improper fraction first.
1. A mixed number [tex]\( -1 \frac{5}{8} \)[/tex] means [tex]\(-1\)[/tex] with an additional [tex]\(\frac{5}{8}\)[/tex].
2. Converting [tex]\( -1 \frac{5}{8} \)[/tex] to an improper fraction involves multiplying the whole number by the denominator and adding the numerator:
[tex]\[
-1 \frac{5}{8} = -\left(1 + \frac{5}{8}\right) = -\left(\frac{8}{8} + \frac{5}{8}\right) = -\left(\frac{8 + 5}{8}\right) = -\frac{13}{8}
\][/tex]
Now, let’s examine the given points on the number line:
- Point A: [tex]\( -2 \)[/tex]
- Point B: [tex]\( -1.5 \)[/tex]
- Point C: [tex]\( -1.625 \)[/tex]
- Point D: [tex]\( -1.75 \)[/tex]
- Point E: [tex]\( -1.875 \)[/tex]
Next, we need to express these decimal values in fractional form for better comparison with [tex]\(-\frac{13}{8}\)[/tex]:
- [tex]\( -2 \)[/tex] is already in its simplest form.
- [tex]\( -1.5 = -\frac{3}{2} = -\frac{12}{8}\)[/tex]
- [tex]\( -1.625 = -1 \frac{625}{1000} = -1 \frac{5/8} = -\frac{13}{8} \)[/tex] (since [tex]\( 0.625 = \frac{5}{8} \)[/tex]). Thus, [tex]\( -1.625 \)[/tex] exactly matches [tex]\(-\frac{13}{8}\)[/tex].
- [tex]\( -1.75 = -\frac{7}{4} = -\frac{14}{8}\)[/tex]
- [tex]\( -1.875 = -\frac{15}{8}\)[/tex]
We can see that [tex]\( -1.625 \)[/tex] matches [tex]\( -\frac{13}{8} \)[/tex]. Therefore, point [tex]\( C \)[/tex] represents [tex]\( -1 \frac{5}{8} \)[/tex] on the number line.
Hence, the correct answer is:
Point C
