Question

plot \\(\sqrt{68}\\) on the decimal number line as accurately as possible.
note that you can use the calculator to help find the answer.
number line from 8 to 9 with evenly spaced ticks

Explanation:

Step1: Find integer bounds

We know that $8^2=64$ and $9^2=81$. Since $64<68<81$, we get $8<\sqrt{68}<9$.

Step2: Calculate decimal value

Compute the exact decimal: $\sqrt{68} \approx 8.246$

Step3: Analyze the number line

The interval between 8 and 9 is split into 10 equal parts, so each mark represents an increment of $0.1$. $8.246$ is between the 2nd and 3rd mark after 8, closer to the 2nd mark (which is 8.2).

Answer:

$\sqrt{68} \approx 8.25$, so it should be plotted 2.5 small intervals to the right of 8 on the given number line (between the 2nd and 3rd tick marks after 8, closer to the 2nd mark).