To arrange the numbers [tex]\(-0.12\)[/tex], [tex]\(-1.2\)[/tex], and [tex]\(-\frac{1}{2}\)[/tex] from least to greatest, we follow these steps:
1. Identify and compare the magnitudes:
- [tex]\(-0.12\)[/tex]: This is a negative number with a value less than zero but close to zero.
- [tex]\(-1.2\)[/tex]: This is a negative number with a value farther from zero (more negative) compared to [tex]\(-0.12\)[/tex].
- [tex]\(-\frac{1}{2}\)[/tex]: This is a negative number. The value of [tex]\(\frac{1}{2}\)[/tex] is 0.5, so [tex]\(-\frac{1}{2}\)[/tex] is equal to [tex]\(-0.5\)[/tex].
2. Compare the values directly:
- [tex]\(-1.2\)[/tex] is more negative than both [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(-0.12\)[/tex], so it is the smallest.
- [tex]\(-\frac{1}{2}\)[/tex] (or [tex]\(-0.5\)[/tex]) is less negative than [tex]\(-1.2\)[/tex] but more negative than [tex]\(-0.12\)[/tex].
- [tex]\(-0.12\)[/tex] is the least negative, making it the largest of the three negative numbers.
3. Arrange in ascending order:
- The smallest (most negative) number is [tex]\(-1.2\)[/tex].
- Next is [tex]\(-\frac{1}{2}\)[/tex] (or [tex]\(-0.5\)[/tex]).
- The largest (least negative) number is [tex]\(-0.12\)[/tex].
So, when arranged from least to greatest, the numbers are:
[tex]\[
-1.2, -0.5, -0.12.
\][/tex]
