Alright! Let's break down the steps to solve the problem:
### Step 1: List the numbers
First, we'll list the numbers given:
[tex]\[ 4, -2, \frac{2}{3}, -1.8, 16, 3.2, -\frac{5}{4} \][/tex]
### Step 2: Separate the numbers into positive and negative values
- Positive numbers: [tex]\( 4, \frac{2}{3}, 16, 3.2 \)[/tex]
- Negative numbers: [tex]\( -2, -1.8, -\frac{5}{4} \)[/tex]
### Step 3: Find the key points
1. Label 0 on the number line:
- This is straightforward; '0' is our reference point.
2. Find the point to the right of 0 (minimum positive number):
- We have to identify the smallest positive number in the positive list: [tex]\( 4, \frac{2}{3}, 16, 3.2 \)[/tex]
- The minimum value among these is [tex]\( \frac{2}{3} \)[/tex].
3. Find the point to the left of 0 (maximum negative number):
- We need to determine the largest (closest to zero) negative number: [tex]\( -2, -1.8, -\frac{5}{4} \)[/tex]
- The maximum value among these is [tex]\( -1.25 \)[/tex] (i.e., [tex]\( -\frac{5}{4} \)[/tex]).
### Step 4: Label the key points on the number line
- '0' is labeled at its reference position.
- The minimum positive number [tex]\( \frac{2}{3} \)[/tex] is labeled to the right of 0.
- The maximum negative number [tex]\( -1.25 \)[/tex] is labeled to the left of 0.
### Summary of the labeled points:
- 0 at the reference point.
- [tex]\( \frac{2}{3} \)[/tex] to the right of 0.
- [tex]\( -1.25 \)[/tex] (i.e., [tex]\( -\frac{5}{4} \)[/tex]) to the left of 0.
This is how you can label these points on a number line with intervals of 1 unit.
