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In Mathematics / Middle School | 2014-08-09

Write each repeating decimal as a fraction in simplest form:

1. [tex]0.\overline{21}[/tex]

Asked by uhhemma16

Answer (2)

0.21212121212121212121...=7/33.
How did I find this out?
n=0.212121212121...
100n=21.212121212121...
100n-n=99n=21
Therefore n=21/99=7/33

Answered by Anonymous | 2024-06-10

The repeating decimal 0. 21 can be expressed as the fraction 33 7 ​ . This is done by setting the decimal equal to a variable, multiplying to align the repeating part, and then solving the resulting equation. After simplifying, we arrive at the final fraction in its simplest form.
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Answered by Anonymous | 2024-09-04

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