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Let x = 10.105105105...
x = 10.105105105... (multiply by 1,000 to both sides)
1,000x = 10,105.105105... (subtract the first equation from the second one)
999x = 10,095 (divide by 999 to both sides)
x = 10,095/999
x = 10,095÷3/999÷3
x = 3,365/333
Thus, 10.105105... = 3,365/333
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