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0.126126126 can be expressed as a repeating decimal, where the 126 pattern repeats indefinitely. To convert this to a fraction, we can set x = 0.126126126 and multiply by 1000 to shift the decimal point three places to the right, yielding 1000x = 126.126126. Subtracting x from 1000x eliminates the repeating decimal, giving 999x = 126. Subtracting the two equations, we get 999x - x = 126 - 0.126, simplifying to 998x = 125.874. Dividing by 998, x = 125.874 / 998 = 2517 / 19900. Therefore, 0.126126126 is equal to 2517/19900 in fraction form.
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