Chapter 0.2, Problem 15E

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 $2\frac{1}{4}$ on real number line is equivalent to $2.25$ so it is closer to 2.

The point that represents $2.\overline{3}$ on real number line is equivalent to $2.33$ so it is next to $2\frac{1}{4}$ .

The point that represents $\sqrt{7}$ on real number line is equivalent to $2.64$ so it is closer to 3.

The point that represents $\sqrt{8}$ on real number line is equivalent to $2.82$ so it is close to 3.

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

So, least is $2\frac{1}{4}$ and greatest is $\sqrt{8}$ .

Numbers ordered from least to greatest as $2\frac{1}{4}<2.\overline{3}<\sqrt{7}<\sqrt{8}$ .