Question

plot \\(\sqrt{46}\\) on the decimal number line as accurately as possible. note that you can use the calculator to help find the answer. your answer (a number line from 6 to 7 with a red eraser icon and some buttons on the side)

Explanation:

Step1: Find integer bounds of $\sqrt{46}$

$6^2=36$, $7^2=49$, so $6<\sqrt{46}<7$

Step2: Calculate decimal value of $\sqrt{46}$

$\sqrt{46}\approx6.782$

Step3: Locate on number line

The interval between 6 and 7 is split into 10 equal parts (each = 0.1). $\sqrt{46}\approx6.78$ is 8 tenths from 6, near the 8th mark.

Answer:

Plot the point 0.78 units to the right of 6 (between the 7th and 8th small tick marks after 6, closer to the 8th mark) on the given number line.