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3 years ago

Write the number 0.21212121 as a fraction

Mathematics

1 answer:

Montano1993 [528]3 years ago

7 0

If is 0.21212121 then

$0.\underbrace{21212121}_{8}=\dfrac{21212121}{1\underbrace{00000000}_{8}}$

If is 0.21212121... then

$x=0.21212121...\ \ \ |\cdot100\\100x=21.21212121...\\\\100x-x=21.21212121...-0.21212121...\\\\99x=21\ \ \ |:99\\\\x=\dfrac{21}{99}\\\\x=\dfrac{21:3}{99:3}\\\\x=\dfrac{7}{33}\\\\0.21212121...=\dfrac{7}{33}$

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