1. **State the problem:** We have two numbers on a number line between 7 and 9 with missing digits: $\_ . 7 \_$ and $\_ . \_ 0$. We must fill in the blanks using the digits 3, 5, 7, and 8 exactly once to complete the numbers. 2. **Analyze the number line:** The numbers lie between 7 and 9, so the integer part of both numbers is likely 7 or 8. 3. **Possible integer parts:** Since the first number is $\_ . 7 \_$, the integer part can be 7 or 8. Similarly for the second number $\_ . \_ 0$. 4. **Use the digits 3, 5, 7, 8 once:** We must assign digits to the blanks so that all four digits are used exactly once. 5. **Try integer part 7 for the first number:** First number: $7.7\_$ Digits left for the last blank: 3, 5, 8 (since 7 is used as integer part and 7 is already in the tenths place) 6. **Try integer part 8 for the second number:** Second number: $8.\_ 0$ Digits left for the tenths place: 3, 5, 7 (since 8 is integer part and 0 is fixed in hundredths place) 7. **Assign digits to satisfy all conditions:** - First number: $7.83$ (using digits 7, 8, 3) - Second number: $8.50$ (using digits 8, 5, 0 but 0 is fixed, so 5 is tenths digit) 8. **Check if all digits 3, 5, 7, 8 are used once:** Digits used: 7, 8, 3, 5 9. **Final numbers:** $$7.83 \quad \text{and} \quad 8.50$$ These fit between 7 and 9 and use all digits exactly once.