0.75 repeating as a fraction'

Answer 1

To express 0.75 repeating (0.757575...) as a fraction, let ( x = 0.757575...). By multiplying both sides by 100, we get ( 100x = 75.757575...). Subtracting the original equation from this gives ( 100x - x = 75.757575... - 0.757575...), leading to ( 99x = 75). Thus, ( x = \frac{75}{99}), which simplifies to ( \frac{25}{33}). Therefore, 0.75 repeating as a fraction is ( \frac{25}{33} ).