The equivalent fraction of the given repeating decimal [tex]0.\overline{3}[/tex] is [tex]\frac{1}{3}[/tex].
How to convert a repeating decimal to a fraction?
A repeating decimal of type [tex]a_0.a_1\overline{a_2a_3}[/tex] can be converted into a fraction as follows: [tex]a_0.a_1\overline{a_2a_3}=a_0+\frac{a_1a_2a_3}{990}[/tex] . As only [tex]a_2[/tex] and [tex]a_3[/tex] are repeated, so the denominator is [tex]990[/tex] i.e., the number of 9's is the same as the number of digits repeated and after that, we put zeros for the non-repeating digits after the decimal point. also, the number of zeros will be the number of non-repeating digits.
Here, the given repeating decimal number is [tex]0.\overline{3}[/tex].
So, its equivalent fraction will be: [tex]0.\overline{3}=\frac{3}{9}=\frac{1}{3}[/tex].
Therefore, the equivalent fraction of the given repeating decimal [tex]0.\overline{3}[/tex] is [tex]\frac{1}{3}[/tex].
To know more about repeating decimal, refer: https://brainly.com/question/99747
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