Sure! Let's walk through locating each given rational number step-by-step.
### (a) [tex]\(\frac{2}{5}\)[/tex]
This is already a simple fraction, and its decimal form is:
[tex]\[
\frac{2}{5} = 0.4
\][/tex]
So, [tex]\(\frac{2}{5}\)[/tex] is located at [tex]\(0.4\)[/tex] on the number line.
### (b) [tex]\(3 \frac{3}{5}\)[/tex]
This mixed number can be converted into decimal form as follows:
First, express the mixed number as an improper fraction.
[tex]\[
3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5}
\][/tex]
Next, convert the improper fraction to a decimal:
[tex]\[
\frac{18}{5} = 3.6
\][/tex]
So, [tex]\(3 \frac{3}{5}\)[/tex] is located at [tex]\(3.6\)[/tex] on the number line.
### (c) [tex]\(2 \frac{4}{5}\)[/tex]
To convert this mixed number into decimal form:
First, express the mixed number as an improper fraction.
[tex]\[
2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5}
\][/tex]
Next, convert the improper fraction to a decimal:
[tex]\[
\frac{14}{5} = 2.8
\][/tex]
So, [tex]\(2 \frac{4}{5}\)[/tex] is located at [tex]\(2.8\)[/tex] on the number line.
### (d) [tex]\(4 \frac{1}{7}\)[/tex]
To convert this mixed number into its decimal form:
First, express the mixed number as an improper fraction.
[tex]\[
4 \frac{1}{7} = \frac{4 \times 7 + 1}{7} = \frac{29}{7}
\][/tex]
Next, convert the improper fraction to a decimal:
[tex]\[
\frac{29}{7} \approx 4.142857142857143
\][/tex]
So, [tex]\(4 \frac{1}{7}\)[/tex] is located at approximately [tex]\(4.142857142857143\)[/tex] on the number line.
By converting each number to its decimal form as shown, we can locate the positions of these rational numbers on a number line.
