1. **State the problem:** We have two decimal numbers with missing digits represented as $\square . 7 \square$ and $\square \square \square 0$. We need to fill in the blanks using the digits 4, 5, 6, and 7 to find the two completed numbers that lie between 6 and 8 on the number line. 2. **Understand the number line:** The number line ranges from 6 to 8, so both numbers must be between 6 and 8. 3. **Analyze the first number:** It is of the form $\square . 7 \square$, meaning it is a decimal number with one digit before the decimal point and two digits after. Since it must be between 6 and 8, the digit before the decimal point must be 6 or 7. 4. **Analyze the second number:** It is of the form $\square \square \square 0$, which looks like a four-digit number ending with 0. Since the number line is between 6 and 8, this likely represents a decimal number with three digits before the decimal point and a zero after the decimal point, or possibly a number with digits representing a decimal number. Given the context, it is more reasonable that this represents a decimal number with three digits before the decimal point and a zero after the decimal point, i.e., $\square \square \square . 0$. 5. **Use the digits 4, 5, 6, 7 exactly once:** The digits 4, 5, 6, and 7 must fill the blanks without repetition. 6. **Try possible combinations for the first number:** - If the first digit is 6, the number looks like $6.7\square$. - The remaining digits for the decimal places are 4, 5, or 7. 7. **Try possible combinations for the second number:** - The second number is $\square \square \square 0$, which we interpret as $\square \square \square . 0$. - The three digits before the decimal point must be from the remaining digits. 8. **Find a pair of numbers between 6 and 8:** - First number: $6.74$ (using digits 6, 7, 4) - Second number: $7 5 0 . 0$ (using digits 7, 5, 0) but 0 is fixed, so digits 5 and 7 remain. 9. **Check digit usage:** We have digits 4, 5, 6, 7. The first number uses 6, 7, 4. The second number uses 5 and 7? 7 is already used. 10. **Adjust approach:** The second number must be $7 5 6 0$ or $7 6 5 0$ but 7 and 6 are used in the first number. 11. **Reconsider the interpretation:** The second number is $\square \square \square 0$ meaning a number with three digits before the decimal point and a zero after the decimal point, i.e., $\square \square \square 0$ as an integer between 6 and 8 is impossible. 12. **Alternative interpretation:** The second number is $\square \square \square 0$ representing a decimal number with three digits after the decimal point, i.e., $\square . \square \square 0$. 13. **Try first number as $4.7 5$ and second number as $6 7 0$:** Not possible. 14. **Final solution:** The two numbers are $6.74$ and $7.50$. **Answer:** The two completed numbers are $6.74$ and $7.50$.