1. **Problem statement:** We need to find the missing values in three lists of rational numbers ordered from least to greatest. 2. **List A:** Given: $0.08$, $\frac{1}{8}$, ____, $20\%$ - Convert all to decimals for easy comparison: - $0.08$ is already decimal. - $\frac{1}{8} = 0.125$ - $20\% = 0.20$ - The missing value must be between $0.125$ and $0.20$. - Choices: $12\% = 0.12$, $\frac{1}{6} \approx 0.1667$, $0.27$ - $0.12$ is less than $0.125$, so it cannot fit between $0.125$ and $0.20$. - $0.27$ is greater than $0.20$, so it cannot fit. - $\frac{1}{6} \approx 0.1667$ fits perfectly between $0.125$ and $0.20$. 3. **List B:** Given: $-\frac{3}{5}$, ____, $-0.55$, $-42\%$ - Convert all to decimals: - $-\frac{3}{5} = -0.6$ - $-0.55$ is decimal. - $-42\% = -0.42$ - The missing value must be between $-0.6$ and $-0.55$. - Choices: $-58\% = -0.58$, $-0.65$, $-\frac{9}{10} = -0.9$ - $-0.65$ and $-0.9$ are less than $-0.6$, so they cannot fit. - $-0.58$ fits between $-0.6$ and $-0.55$. 4. **List C:** Given: $600\%$, ____, $6 \frac{2}{3}$, $6.9$ - Convert all to decimals: - $600\% = 6.00$ - $6 \frac{2}{3} = 6 + \frac{2}{3} = 6.6667$ - $6.9$ is decimal. - The missing value must be between $6.00$ and $6.6667$. - Choices: $60.2$, $\frac{19}{3} \approx 6.3333$, $6.95$ - $60.2$ and $6.95$ are greater than $6.6667$, so they cannot fit. - $\frac{19}{3} \approx 6.3333$ fits between $6.00$ and $6.6667$. **Final answers:** - List A missing value: $\frac{1}{6}$ - List B missing value: $-58\%$ - List C missing value: $\frac{19}{3}$