Write the repeating decimal as a fraction

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

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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