Example 4 from Algebra and Trigonometry, 1.1 Real Numbers: Algebra Essentials

Classifying Real Numbers

Classify each number as either positive or negative and as either rational or irrational. Does the number lie to the left or the right of 0 on the number line?

ⓐ $- \frac{10}{3}$
ⓑ $\sqrt{5}$
ⓒ $- \sqrt{289}$
ⓓ $−6 π$
ⓔ $0.615384615384 \dots$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ $- \frac{10}{3}$ is negative and rational. It lies to the left of 0 on the number line.
2. ⓑ $\sqrt{5}$ is positive and irrational. It lies to the right of 0.
3. ⓒ $- \sqrt{289} = - \sqrt{17^{2}} = −17$ is negative and rational. It lies to the left of 0.
4. ⓓ $−6 π$ is negative and irrational. It lies to the left of 0.
5. ⓔ $0.615384615384 \dots$ is a repeating decimal so it is rational and positive. It lies to the right of 0.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Classify each number as either positive or negative and as either rational or irrational. Does the number lie to the left or the right of 0 on the number line?

ⓐ $\sqrt{73}$
ⓑ $−11.411411411 \dots$
ⓒ $\frac{47}{19}$
ⓓ $- \frac{\sqrt{5}}{2}$
ⓔ $6.210735$

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Classify each number as either positive or negative and as either rational or irrational. Does the number lie to the left or the right of 0 on the number line?

ⓐ $\sqrt{73}$
ⓑ $−11.411411411 \dots$
ⓓ $- \frac{\sqrt{5}}{2}$
ⓔ $6.210735$

Solution

Your turn

Solution

Your turn