To plot the given numbers accurately on a number line, we first convert any fractions to their decimal equivalents for ease of placement. Here are the numbers provided:
1. [tex]\( \frac{2}{4} \)[/tex] which simplifies to [tex]\( 0.5 \)[/tex]
2. [tex]\( 1.25 \)[/tex]
3. [tex]\( 0.8 \)[/tex]
4. [tex]\( \frac{4}{3} \)[/tex] which simplifies to approximately [tex]\( 1.3333333333333333 \)[/tex]
5. [tex]\( 1.6 \)[/tex]
Now, let’s place these numbers on a number line.
### Step-by-Step Placement:
1. [tex]\( 0.5 \)[/tex]: This number is halfway between 0 and 1.
2. [tex]\( 1.25 \)[/tex]: This number is slightly more than 1. It is exactly one and one-fourth, so it is placed a quarter way past 1.
3. [tex]\( 0.8 \)[/tex]: This number is just less than 1, specifically four-fifths between 0 and 1.
4. [tex]\( 1.3333333333333333 \)[/tex]: This number is approximately one and one-third, so it is placed one-third of the way past 1.
5. [tex]\( 1.6 \)[/tex]: This number is simple to place as it is just a bit less than 2, being six-tenths of the way there.
Here is a rough number line with the points marked:
```
0 0.5 1 1.25 1.3333 1.6 2
|------|-------|-------|----------|-----------|------|
```
- Each vertical line (|) represents an interval on the number line.
- The points between 0 and 2 are plotted based on the approximate positions calculated:
- [tex]\(0.5\)[/tex] is halfway.
- [tex]\(1.25\)[/tex] is a quarter past 1.
- [tex]\(0.8\)[/tex] is close to but less than 1.
- [tex]\(1.3333\)[/tex] is roughly one-third past 1.
- [tex]\(1.6\)[/tex] is closer to 2 but not quite there yet.
In summary, plotting each of these decimals on the number line ensures that they are accurately represented relative to one another.
