Question

writing locate $-sqrt{15}$ 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 $-sqrt{15}$. (number line from -5 to 0 with ticks at -4, -3, -2, -1, 0)

Explanation:

Step1: Find $\sqrt{15}$ estimate

$\sqrt{9}=3$, $\sqrt{16}=4$, so $\sqrt{15}\approx3.872$

Step2: Negate the value

$-\sqrt{15}\approx-3.872$

Step3: Round to nearest tenth

$-3.872\approx-3.9$

Step4: Explain decimal use

Exact $-\sqrt{15}$ is irrational; a decimal estimate gives a precise, easy-to-locate position on a labeled number line with tenths intervals, since irrational numbers cannot be plotted exactly with standard tick marks.

Answer:

$-3.9$ (located between $-4$ and $-3$, closer to $-4$ on the number line)