Question

Express this decimal as a fraction.
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Answer 1

`\large\boxed{1.\overline{21}=(40)/(33)}`

Explanation:

`x=1.\overline{21}\\\\x=1.212121...\qquad\text{multiply both sides by 100}\\\\100x=121.212121...\\\\\text{subtract x from 100x}\\\\100x-x=121.212121...-1.212121...\\\\99x=120\qquad\text{divide both sides by 99}\\\\x=(120)/(99)\\\\x=(120:3)/(99:3)\\\\x=(40)/(33)`