Chapter 0.2, Problem 14E

To determine

To graph: The set of real numbers $\left\{\frac{1}{2},-\frac{7}{9},\frac{1}{9},-\frac{4}{9}\right\}$ and order the numbers from least to greatest.

Explanation of Solution

Given information:

The set of real numbers $\left\{\frac{1}{2},-\frac{7}{9},\frac{1}{9},-\frac{4}{9}\right\}$ .

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 $\left\{\frac{1}{2},-\frac{7}{9},\frac{1}{9},-\frac{4}{9}\right\}$ and mark them with dot.

The obtained number line is provided below,

  

Interpretation:

The point that represents $-\frac{7}{9}$ on real number line is equivalent to $-0.7$ so it is closer to $-1$ .

The point that represents $-\frac{4}{9}$ on real number line is equivalent to $-0.4$ so it is closer to $0$ on left hand side.

The point that represents $\frac{1}{9}$ on real number line is equivalent to $0.1$ so it is closer to 0 on right hand side.

The point that represents $\frac{1}{2}$ on real number line is equivalent to $0.5$ so it is between 0 and 1.

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

So, least is $-\frac{7}{9}$ and greatest is $\frac{1}{2}$ .

Numbers ordered from least to greatest as $\frac{-7}{9}<\frac{-4}{9}<\frac{1}{9}<\frac{1}{2}$ .