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The completed pattern is:
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The pattern in the equations involves dividing a number, represented by the square, by increasing powers of 10. The first equation shows that if you divide the square by 10, you get 7.764. For the second equation, dividing by 1,000 gives 0.07764, which is 7.764 divided by 10. The third equation, dividing by 10,000 yields 0.007764, again dividing the previous result by 10.
Continuing this pattern, the next equations can be deduced:
Now, to find the value represented by the square, we can backtrack from 7.764. Since
, then
.
Thus, the completed pattern would represent: