What is 0.08 recurring as a fraction?

Answer 1

To convert 0.08 recurring (0.088888...) into a fraction, let ( x = 0.08\overline{8} ). Multiplying both sides by 10 gives ( 10x = 0.8\overline{8} ). Subtracting the original ( x ) from this equation results in ( 9x = 0.8 ), leading to ( x = \frac{0.8}{9} ). Since ( 0.8 = \frac{8}{10} = \frac{4}{5} ), we find ( x = \frac{4}{5} \times \frac{1}{9} = \frac{4}{45} ). Thus, 0.08 recurring as a fraction is ( \frac{4}{45} ).