Question

writing locate $-sqrt{6}$ to the nearest tenth on a number line. use pencil and paper. explain why it might be better to use a decimal estimate instead of an exact value to plot this number on a number line.
move the point to the tick mark that is closest to $-sqrt{6}$.

Explanation:

Step1: Estimate $\sqrt{6}$

$\sqrt{4}=2$, $\sqrt{9}=3$, so $\sqrt{6}\approx2.45$

Step2: Find $-\sqrt{6}$

$-\sqrt{6}\approx-2.45$

Step3: Round to nearest tenth

$-2.45$ rounds to $-2.5$

Step4: Explain decimal use

Number lines use decimal ticks, so decimal estimates match the tick marks exactly, making plotting precise, while the exact radical form does not correspond to a labeled tick on the standard number line.

Answer:

1. The tick mark closest to $-\sqrt{6}$ is $-2.5$.
2. Using a decimal estimate is better because number lines are marked with decimal/ integer tick marks, so the decimal estimate aligns directly with a labeled position, making plotting accurate and straightforward, whereas the exact radical $-\sqrt{6}$ does not match a standard labeled tick.