Question

(a) plot $2pi$ and $4sqrt{3}$ on the decimal number line. note that you can use the calculator.
(b) based on your answer above, compare $2pi$ and $4sqrt{3}$ using $<$, $>$, or $=$.
$2pi \square 4sqrt{3}$

Explanation:

Part (a)

Step1: Calculate \( 2\pi \)

We know that \( \pi \approx 3.1416 \), so \( 2\pi = 2\times3.1416 = 6.2832 \).

Step2: Calculate \( 4\sqrt{3} \)

We know that \( \sqrt{3}\approx1.732 \), so \( 4\sqrt{3}=4\times1.732 = 6.928 \).
To plot on the number line:

• \( 2\pi\approx6.2832 \) is between \( 6.2 \) and \( 6.3 \) (closer to \( 6.3 \)).
• \( 4\sqrt{3}\approx6.928 \) is between \( 6.9 \) and \( 7 \) (closer to \( 6.9 \)).

Part (b)

From the calculations in part (a), \( 2\pi\approx6.2832 \) and \( 4\sqrt{3}\approx6.928 \). Since \( 6.2832<6.928 \), we can compare them.

Answer:

(a) Plot \( 2\pi\approx6.28 \) (between \( 6.2 \) and \( 6.3 \)) and \( 4\sqrt{3}\approx6.93 \) (between \( 6.9 \) and \( 7 \)) on the number line.
(b) \( 2\pi\ <\ 4\sqrt{3} \) (select the \( < \) option with \( 2\pi \) and \( 4\sqrt{3} \) in the boxes: \( 2\pi < 4\sqrt{3} \))