Question

plot $2\frac{4}{5}$ and $1\frac{7}{10}$.

Explanation:

Step1: Analyze the number line

The number line has marks from 0 to 3. Let's first find the length of each small segment. From 0 to 1, 1 to 2, and 2 to 3, we can assume the number of segments between two integers. Let's convert the mixed numbers to improper fractions or decimals for easier plotting.

First, for \(2\frac{4}{5}\):
\(2\frac{4}{5}=\frac{2\times5 + 4}{5}=\frac{14}{5}=2.8\)

For \(1\frac{7}{10}\):
\(1\frac{7}{10}=\frac{1\times10+7}{10}=\frac{17}{10} = 1.7\)

Now, let's see the number of segments between 0 and 1, 1 and 2, 2 and 3. Let's assume that between each integer (e.g., 0 - 1, 1 - 2, 2 - 3), there are 10 small segments (since the denominators are 5 and 10, 10 is a common denominator). So each small segment represents \( \frac{1}{10}=0.1\).

Step2: Plot \(1\frac{7}{10}=1.7\)

Starting from 1, we move 7 segments to the right (since \(0.7=\frac{7}{10}\), and each segment is 0.1). So from 1, moving 7 steps (each 0.1) gets us to \(1 + 0.7=1.7\).

Step3: Plot \(2\frac{4}{5}=2.8\)

Starting from 2, we move 8 segments to the right (since \(0.8=\frac{4}{5}=\frac{8}{10}\), and each segment is 0.1). So from 2, moving 8 steps (each 0.1) gets us to \(2+0.8 = 2.8\).

Answer:

To plot \(2\frac{4}{5}\) (which is \(2.8\)): Start at 2, move 8 small segments (each representing \(0.1\)) to the right.
To plot \(1\frac{7}{10}\) (which is \(1.7\)): Start at 1, move 7 small segments (each representing \(0.1\)) to the right.

(Note: Since this is a plotting task, the final answer describes the positions on the number line as calculated above.)