Chapter 1 - Foundations for Algebra - 1-3 Real Numbers and the Number Line - Practice and Problem-Solving Exercises - Page 20: 43

$-0.\overline8\lt-\frac{22}{25}$

Restate the fraction as a decimal to compare. $-\frac{22}{25}=\,-0.88\underset\uparrow0$ $-0.\overline8=-0.88\underset\uparrow8\overline8$ Comparing the thosandths position, $-0.\overline8$ has the largest absolute value. Since the numbers are negative, $-0.\overline8$ is the smaller number.