Chapter 0.2, Problem 16E

To determine

To graph: The set of real numbers $\left\{2\frac{1}{4},\sqrt{7},2.\overline{3},\sqrt{8}\right\}$ and order the numbers from least to greatest.

Explanation of Solution

Given information:

The set of real numbers $\left\{2\frac{1}{4},\sqrt{7},2.\overline{3},\sqrt{8}\right\}$ .

Graph:

Construct a real number line. Mark the negative integers on left of zero and positive integers on right of zero.

Plot the set of real numbers $\left\{2\frac{1}{4},\sqrt{7},2.\overline{3},\sqrt{8}\right\}$ and mark them with dot.

The obtained number line is provided below,

  

Interpretation:

The point that represents $0.\overline{1}$ on real number line is equivalent to $0.111$ so it is closer to 0.

The point that represents $\frac{4}{5}$ on real number line is equivalent to $0.8$ so it is close to 1.

The point that represents $\sqrt{2}$ on real number line is equivalent to $1.41$ so it is closer to 1.

The point that represents $\sqrt{3}$ on real number line is equivalent to $1.73$ so it is close to 2.

Now, real number line depicts integers in ascending order that is from least to greatest.

So, least is $0.\overline{1}$ and greatest is $\sqrt{3}$ .

Numbers ordered from least to greatest as $0.\overline{1}<\frac{4}{5}<\sqrt{2}<\sqrt{3}$ .