Exercicios Sobre Fração — Geratriz

(0.3\overline18) (x = 0.3181818\ldots) Multiply by 10: (10x = 3.181818\ldots) (now pure repeating: (3.\overline18)) (1000x = 318.181818\ldots) (since (10x \times 100 = 1000x)) Wait — better method: Let (x = 0.3\overline18) Multiply by 10: (10x = 3.\overline18) (pure repeating) Now (10x = 3 + 0.\overline18) (0.\overline18 = \frac1899 = \frac211) So (10x = 3 + \frac211 = \frac33+211 = \frac3511) Thus (x = \frac35110 = \frac722)

| Type | Description | Example | |------|-------------|---------| | Terminating decimal | Ends after finite digits | (0.25 = \frac14) | | Pure repeating decimal | All digits after the decimal point repeat | (0.\overline142857 = \frac17) | | Mixed repeating decimal | Some non-repeating digits followed by a repeating block | (0.1\overline6 = \frac16) | exercicios sobre fração geratriz