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arletsolis23p2cjls

18.11.2020

Mathematics

$\large\boxed{1.\overline{21}=\dfrac{40}{33}}$

Step-by-step explanation:

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

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