Write the repeating decimal as a fraction

Show that the repeating decimal .234234234 can be written as a fraction.

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x = .234234234   {let x equal the given repeating decimal}

1,000x = 234.234234234   {multiplied both sides by 1,000}
            x = .234234234   {original equation}
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999x = 234   {subtracted the two equations}
x = 234/999   {divided both sides by 999}
x = 26/111   {reduced}

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