Complete the pattern: \( \begin{array}{l}\square \div 10=7.764 \\ \square \div 1,000=0.07764 \\ \square \div 10,000=0.007764 \\ \square 100,000=0.0007764\end{array} \)

The pattern shows that the value in the square is consistently being divided by increasing powers of ten, resulting in a decimal being formed. To solve for the square, we can start from the first equation: \[ \square = 7.764 \times 10 \] This gives us: \[ \square = 77.64 \] So, the value in the square is 77.64. Now let's verify by substituting it back into the remaining equations: 1. For \(\square \div 1,000\): \[ 77.64 \div 1,000 = 0.07764 \] Correct! 2. For \(\square \div 10,000\): \[ 77.64 \div 10,000 = 0.007764 \] Correct! 3. For \(\square \div 100,000\): \[ 77.64 \div 100,000 = 0.0007764 \] Correct! So, the completed pattern results in \(\square = 77.64\).