Rational Number Line 648A66

1. **Problem Statement:** Plot the given numbers $$\frac{13}{20}$$, $$-\frac{1}{7}$$, $$0.40$$, $$10\%$$, and $$2.25$$ on a number line and identify their positions as rational numbers. 2. **Convert all numbers to rational form:** - $$\frac{13}{20}$$ is already a fraction. - $$-\frac{1}{7}$$ is already a fraction. - $$0.40 = \frac{40}{100} = \frac{2}{5}$$ after simplification. - $$10\% = \frac{10}{100} = \frac{1}{10}$$. - $$2.25 = 2 + 0.25 = 2 + \frac{1}{4} = \frac{9}{4}$$. 3. **Order the numbers from smallest to largest:** - $$-\frac{1}{7} \approx -0.1429$$ - $$\frac{1}{10} = 0.1$$ - $$\frac{2}{5} = 0.4$$ - $$\frac{13}{20} = 0.65$$ - $$\frac{9}{4} = 2.25$$ 4. **Plotting on the number line:** - Start from negative values, place $$-\frac{1}{7}$$ slightly left of zero. - Place $$\frac{1}{10}$$ just right of zero. - Place $$\frac{2}{5}$$ further right. - Place $$\frac{13}{20}$$ even further right. - Place $$\frac{9}{4}$$ well to the right, beyond 2. 5. **Summary:** All given numbers are rational and can be represented as fractions. **Final answer:** The numbers in order on the number line are $$-\frac{1}{7} < \frac{1}{10} < \frac{2}{5} < \frac{13}{20} < \frac{9}{4}$$.