Question

(a) plot $7\sqrt{2}$ and $3\pi$ on the decimal number line.
note that you can use the calculator.

(b) based on your answer above, compare $7\sqrt{2}$ and $3\pi$ using $<$, $>$, or $=$.
$7\sqrt{2} \square 3\pi$

Explanation:

Step1: Calculate decimal value of $7\sqrt{2}$

$7\sqrt{2} \approx 7\times1.4142 = 9.8994$

Step2: Calculate decimal value of $3\pi$

$3\pi \approx 3\times3.1416 = 9.4248$

Step3: Plot values on number line

• Mark $3\pi \approx 9.42$ between 9.4 and 9.5
• Mark $7\sqrt{2} \approx 9.90$ between 9.9 and 10

Step4: Compare the two values

Since $9.8994 > 9.4248$, $7\sqrt{2} > 3\pi$

Answer:

(a)

• $3\pi \approx 9.42$ is plotted between 9.4 and 9.5 on the number line
• $7\sqrt{2} \approx 9.90$ is plotted between 9.9 and 10 on the number line

(b) $7\sqrt{2} > 3\pi$