Chapter 1.2, Problem 57PPSE

Solution

To state: The numbers $1,-3,-\sqrt{2},8,and\frac{1}{3}$ in decreasing order.

The resultant answer is $8>1>\frac{1}{3}>-\sqrt{2}>-3$ .

Given information:

The given numbers are $1,-3,-\sqrt{2},8,and\frac{1}{3}$ .

Explanation:

Consider the given numbers:

Find the approximate decimal values of each given rational and irrational numbers to compare numbers easily,

  $\begin{array}{c}-\sqrt{2}\approx -1.414\\ \frac{1}{3}\approx 1.33\end{array}$

Now arrange the numbers is decreasing order which means to arrange numbers from greatest to smallest numbers.

  $8>1>1.33>-1.414>-3$

Now replace these numbers with original numbers,

  $8>1>\frac{1}{3}>-\sqrt{2}>-3$

Therefore, the numbers are $8>1>\frac{1}{3}>-\sqrt{2}>-3$ .