Cody has started running in a well-organized manner. He runs 100 m east, then turns left...

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Cody has started running in a well-organized manner. He runs 100 m east, then turns left and runs another 10 m north, turns left and runs 1 m, again turns left and runs 0.1 m, and on the next turn 0.01 m, and so on. Assuming that Cody can run in this pattern infinitely, the displacement from his initial position can be written as with a and b being positive integers and b square-free. What is the value of a x b? Cody has started running in a well-organized manner. He runs 100 m east, then turns left and runs another 10 m north, turns left and runs 1 m, again turns left and runs 0.1 m, and on the next turn 0.01 m, and so on. Assuming that Cody can run in this pattern infinitely, the displacement from his initial position can be written as with a and b being positive integers and b square-free. What is the value of a x b?

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