Complete the pattern: \( \begin{array}{r}\square \div 10=7.764 \\ \square \div 1,000=0.07764 \\ \square \div 10,000=0.007764 \\ \square \\ \square\end{array} \)

To complete the pattern, we first need to identify the value of the square (\(\square\)) in the equations provided. 1. From the first equation: \[ \square \div 10 = 7.764 \] We can find \(\square\) by multiplying both sides by 10: \[ \square = 7.764 \times 10 = 77.64 \] 2. Now, let's verify this value with the second equation: \[ \square \div 1,000 = 0.07764 \] Substituting \(\square = 77.64\): \[ 77.64 \div 1,000 = 0.07764 \] This is correct. 3. Next, we check the third equation: \[ \square \div 10,000 = 0.007764 \] Again substituting \(\square = 77.64\): \[ 77.64 \div 10,000 = 0.007764 \] This is also correct. Now, we can complete the pattern for the next two squares: 4. For the fourth square, we can follow the pattern of dividing by 100,000: \[ \square \div 100,000 = \frac{77.64}{100,000} = 0.0007764 \] 5. For the fifth square, we can follow the pattern of dividing by 1,000,000: \[ \square \div 1,000,000 = \frac{77.64}{1,000,000} = 0.00007764 \] Thus, the completed pattern is: \[ \begin{array}{r} 77.64 \div 10 = 7.764 \\ 77.64 \div 1,000 = 0.07764 \\ 77.64 \div 10,000 = 0.007764 \\ 77.64 \div 100,000 = 0.0007764 \\ 77.64 \div 1,000,000 = 0.00007764 \end{array} \]