Question

standard: (8.nr.1.2)
consider the numbers \\(\sqrt{6}, 1.8, \sqrt{25}, \frac{1}{3}, \pi, 6\\).
which of the following shows the numbers graphed and listed in order from least to greatest?
\\(\frac{1}{3}, 1.8, \sqrt{6}, \pi, \sqrt{25}, 6\\)
\\(\frac{1}{3}, 1.8, \pi, \sqrt{6}, \sqrt{25}, 6\\)
\\(\frac{1}{3}, 1.8, \pi, \sqrt{6}, \sqrt{25}, 6\\)
\\(\frac{1}{3}, 1.8, \sqrt{6}, \pi, \sqrt{25}, 6\\)

Explanation:

Step1: Calculate each value

$\frac{1}{3}\approx0.33$, $\sqrt{6}\approx2.45$, $\sqrt{25}=5$, $\pi\approx3.14$, $1.8=1.8$, $6=6$

Step2: Order from least to greatest

$0.33 < 1.8 < 2.45 < 3.14 < 5 < 6$, so $\frac{1}{3} < 1.8 < \sqrt{6} < \pi < \sqrt{25} < 6$

Step3: Match to number line

Plot values: $\frac{1}{3}$ near 0, $1.8$ near 2, $\sqrt{6}$ near 2.5, $\pi$ near 3, $\sqrt{25}=5$, $6$ at 6, which matches the last option's number line.

Answer:

$\frac{1}{3}, 1.8, \sqrt{6}, \pi, \sqrt{25}, 6$ (with the corresponding number line: $\longleftarrow\underset{0}{\bullet}\underset{1}{\bullet}\underset{2}{\bullet}\underset{3}{\bullet}\hspace{1em}\underset{5}{\bullet}\underset{6}{\bullet}\longrightarrow$)