Practice Solutions

Plot the rational numbers on a number line.

$- \frac{1}{3}$

$- \frac{5}{3}$

$\frac{4}{3}$

Note

Q: What is the scale? 

A: The scale is $\frac{1}{3} .$

–4

–10

Note

Q: What is the scale?

A: The scale is 2.

Q: Where would you plot –3?

A: Halfway between –2 and –4.

Plot and label the real numbers on a number line. Label with the original form of the number.

100%

$\sqrt{3}$

$- \sqrt{11}$

$100 % = 1, \sqrt{3} \approx 1.73, - \sqrt{11} \approx - 3.32$

3.52

$π$

$- \sqrt{4}$

$π \approx 3.14, - \sqrt{4} = - 2$

Note

Q: Are all square roots irrational numbers?

A: No, square roots that are perfect squares are rational numbers.

$- \frac{5}{2}$

$\frac{1}{5}$

$\sqrt{5}$

$- \frac{5}{2} = - 2.5, \frac{1}{5} = 0.2, \sqrt{5} \approx 2.24$

Compare the rational and irrational numbers using greater than or less than.

$3 > \sqrt{3}$

$\sqrt{3} \approx 1.7321$

$\sqrt{17} < 4.5$

$\sqrt{17} \approx 4.1231$

$\sqrt{6} < 2.5$

$\sqrt{6} \approx 2.4495$

$\frac{26}{3} < \sqrt{77}$

$\frac{26}{3} = 8.6 \sqrt{77} \approx 8.7750$

$π > 3.14$

$π \approx 3.1416$

Note

The irrational number pi is infinite. The decimal approximation to the nearest hundredth is 3.14. An irrational number cannot equal a rational number.

$- 5 < - \sqrt{5}$

$- \sqrt{5} \approx - 2.2361$

$- \frac{7}{8} > - \sqrt{7}$

$- \frac{7}{8} = - 0.875 - \sqrt{7} \approx - 2.6458$