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Question 4

Let $$x$$ be the number $$0.000\ldots001$$ which has 2019 zeroes after the decimal point. Then which of the following numbers is the greatest?

Since $$x=10^{-2020}$$ is extremely small, $$10000+x$$ and $$10000-x$$ are both close to 10000, while $$\frac{10000}{x}=10^{2024}$$ is enormous, but $$\frac{1}{x^2}=10^{4040}$$ is far larger still.

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