To identify the location for each of the given points on the number line, we'll convert all the given numbers to decimal form and identify the corresponding points.
1. [tex]$-\frac{1}{10}$[/tex]: Let's convert this rational number to a decimal:
[tex]\[
-\frac{1}{10} = -0.1
\][/tex]
Thus, [tex]$-\frac{1}{10}$[/tex] corresponds to -0.1 on the number line.
2. [tex]$\frac{1}{5}$[/tex]: Convert this rational number to a decimal:
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
Thus, [tex]$\frac{1}{5}$[/tex] corresponds to 0.2 on the number line.
3. [tex]$\frac{9}{10}$[/tex]: Convert this rational number to a decimal:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
Thus, [tex]$\frac{9}{10}$[/tex] corresponds to 0.9 on the number line.
4. -0.5: This is already in decimal form and corresponds directly to -0.5 on the number line.
5. 0.6: This is already in decimal form and corresponds directly to 0.6 on the number line. Looking at the list, 0.6 corresponds to point D.
6. [tex]$-\frac{4}{5}$[/tex]: Convert this rational number to a decimal:
[tex]\[
-\frac{4}{5} = -0.8
\][/tex]
Thus, [tex]$-\frac{4}{5}$[/tex] corresponds to -0.8 on the number line.
Based on these conversions, the matching for point D is as follows:
- 5. 0.6 corresponds to D
The remaining mapping of points is:
- 1. [tex]$-\frac{1}{10}$[/tex] corresponds to -0.1
- 2. [tex]$\frac{1}{5}$[/tex] corresponds to 0.2
- 3. [tex]$\frac{9}{10}$[/tex] corresponds to 0.9
- 4. -0.5 is already given as B
- 6. [tex]$-\frac{4}{5}$[/tex] corresponds to -0.8 with label A
So the full match is:
6. 0.6 D
