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Question

If 0.42 is written as a fraction ab where a and b are positive integers with a greatest common divisor of 1, what is a+b?

Accepted Answer

Let x = 0.42. Multiplying both sides by 100, we get 100x = 42.42. Subtracting these two equations gives 99x = 42, so x = 4299 = 1433. Thus a+b = 14+33 = 47.