To determine between which two numbers [tex]\(-\frac{2}{3}\)[/tex] is located on a number line, let's break it down step-by-step:
1. Understand the Fraction: First, [tex]\(-\frac{2}{3}\)[/tex] is a negative fraction.
2. Convert to Decimal: Converting [tex]\(-\frac{2}{3}\)[/tex] to a decimal will help us place it more accurately on the number line. When we convert, we get [tex]\(-0.666...\)[/tex].
3. Compare with Given Intervals:
- -4 and -3: [tex]\(-0.666...\)[/tex] is not between [tex]\(-4\)[/tex] and [tex]\(-3\)[/tex] because it is much closer to 0 than to [tex]\(-4\)[/tex] or [tex]\(-3\)[/tex].
- -3 and -2: [tex]\(-0.666...\)[/tex] is not between [tex]\(-3\)[/tex] and [tex]\(-2\)[/tex] because, similar to the previous step, it is closer to 0.
- -2 and -1: [tex]\(-0.666...\)[/tex] is not between [tex]\(-2\)[/tex] and [tex]\(-1\)[/tex] because it is greater than [tex]\(-2\)[/tex] and closer to 0.
- -1 and 0: [tex]\(-0.666...\)[/tex] lies perfectly between [tex]\(-1\)[/tex] and 0. Indeed, [tex]\(-0.666...\)[/tex] is greater than [tex]\(-1\)[/tex] and less than 0.
Thus, [tex]\(-\frac{2}{3}\)[/tex], which is [tex]\(-0.666...\)[/tex], is located on the number line between [tex]\(-1\)[/tex] and 0.
