Certainly! To represent the expression \(\sqrt{3} \times 0.5\) on the number line, we need to follow a series of steps:
1. Understanding \(\sqrt{3}\):
The square root of 3 is approximately 1.732. This is an irrational number, but for our purposes, we'll use the given approximation.
2. Calculation of the Product:
We need to multiply \(\sqrt{3}\) by 0.5.
[tex]\[
\begin{aligned}
\sqrt{3} &\approx 1.732 \\
0.5 \times 1.732 &= 0.866
\end{aligned}
\][/tex]
Thus, \(\sqrt{3} \times 0.5 = 0.866\).
3. Locate 0.866 on the Number Line:
To represent 0.866 on the number line:
- First, identify the section of the number line between 0 and 1.
- Since 0.866 is closer to 1 than to 0, it will be found in the interval between 0.8 and 0.9.
- Further refine to place 0.866 between these two points.
4. Steps to Place Correctly:
- Mark 0, 1, and the midpoints 0.5, and then further points like 0.1, 0.2, 0.3 etc., up to 1.
- Once you have 0.8 and 0.9 marked, 0.866 would be slightly closer to 0.9 than 0.8.
5. Final Placement:
You will mark a point on the number line slightly closer to 0.9 than 0.8 to represent 0.866.
Here's a basic representation of the number line with 0.866 marked:
```
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
|----|----|----|----|----|----|----|----|----|----|----|
(≈ 0.866)
```
The star () denotes the approximate location of 0.866 on the number line.
By following these steps, you accurately place [tex]\(\sqrt{3} \times 0.5\)[/tex] on the number line.
