Chapter 0.2, Problem 17E

To determine

To graph: The set of real numbers $\left\{-3.5,-\frac{15}{5},-\sqrt{10},-3\frac{3}{4}\right\}$ and order the numbers from least to greatest.

Explanation of Solution

Given information:

The set of real numbers $\left\{-3.5,-\frac{15}{5},-\sqrt{10},-3\frac{3}{4}\right\}$ .

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 $\left\{-3.5,-\frac{15}{5},-\sqrt{10},-3\frac{3}{4}\right\}$ and mark them with dot.

The obtained number line is provided below,

  

Interpretation:

The point that represents $-3\frac{3}{4}$ on real number line is equivalent to $-3.75$ so it is closer to $-4$ .

The point that represents $-3.5$ on real number line is equivalent to $-3.5$ so it is between $-3$ and $-4$ .

The point that represents $-\sqrt{10}$ on real number line is equivalent to $-3.16$ so it is closer to $-3$ .

The point that represents $\frac{-15}{5}$ on real number line is equivalent to $3$ .

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

So, least is $-3\frac{3}{4}$ and greatest is $\frac{-15}{5}$ .

Numbers ordered from least to greatest as $-3\frac{3}{4}<-3.5<-\sqrt{10}<-\frac{15}{5}$ .