1. **State the problem:** We have four digits 3, 5, 7, 8 to fill in the missing places in two decimal numbers on a number line between 7 and 9. The numbers are of the form $[\_].7[\_]$ and $[\_].[\_]0$. 2. **Analyze the number line:** The number line ranges from 7 to 9, and the two numbers must lie between these values. 3. **Consider the first number $[\_].7[\_]$:** - The integer part must be 7 or 8 because the number is between 7 and 9. - The decimal part is 7 followed by a missing digit. 4. **Consider the second number $[\_].[\_]0$:** - The integer part must be 7 or 8. - The decimal part ends with 0. 5. **Use the digits 3, 5, 7, 8 exactly once:** - Assign digits to the blanks so that both numbers are between 7 and 9. 6. **Try integer part 7 for both:** - First number: 7.7[\_], second number: 7.[\_]0 - Remaining digits for decimal places: 3, 5, 8 (since 7 is used in decimal already) 7. **Assign digits:** - First number decimal: 7.73 or 7.75 or 7.78 - Second number decimal: 7.50, 7.80, 7.30 8. **Check which combinations use all digits 3,5,7,8 once:** - If first number is 7.73 (digits used: 7,7,3), second number must use 5 and 8. - Second number: 7.80 (digits 7,8,0) but 0 is fixed, so digits used are 7 and 8. - Digits used: 3,5,7,8. Here 5 is unused. - Try first number 7.75 (digits 7,7,5), second number 7.30 (digits 7,3,0) - Digits used: 3,5,7,7 (7 repeated), but only one 7 card is given. - Try first number 7.78 (digits 7,7,8), second number 7.30 (digits 7,3,0) - Digits used: 3,7,8,7 (7 repeated), invalid. 9. **Try integer part 8 for first number:** - First number: 8.7[\_], second number: 7.[\_]0 - Digits left: 3,5,7,8 - First number decimal: 8.73 or 8.75 or 8.78 - Second number decimal: 7.50, 7.30, 7.70 10. **Check combinations:** - First number 8.73 (digits 8,7,3), second number 7.50 (digits 7,5,0) - Digits used: 3,5,7,8 all used once. 11. **Verify both numbers are between 7 and 9:** - 8.73 is between 7 and 9. - 7.50 is between 7 and 9. 12. **Final answer:** - The two completed numbers are $8.73$ and $7.50$.