Answer:
[tex]\dfrac{1213}{9999}[/tex]
Step-by-step explanation:
We are required to express [tex]0.\overline{1}+0.\overline{01}+0.\overline{0001}[/tex] as a common fraction.
The bar on top of the decimal part indicates the decimal number is a repeating decimal.
Therefore:
[tex]0.\overline{1}=\dfrac{1}{10-1}= \dfrac{1}{9}\\\\0.\overline{01}=\dfrac{1}{100-1}= \dfrac{1}{99}\\\\0.\overline{0001}=\dfrac{1}{10000-1}= \dfrac{1}{9999}\\\\\\$Therefore$:\\0.\overline{1}+0.\overline{01}+0.\overline{0001} \\=\dfrac{1}{9}+\dfrac{1}{99}+\dfrac{1}{9999}\\\\=\dfrac{1213}{9999}[/tex]
