91影视

To convert the repeating decimal $$0 . \overline{3}$$ to a fraction, we'll let $$x$$ represent the decimal. Since the number $$3$$ is repeating, we can write the decimal as a geometric series: $$x = 0.333... = 3 \times 10^{-1} + 3 \times 10^{-2} + 3 \times 10^{-3} + ...$$ Now, we can use the formula for the sum of an infinite geometric series: $$S = \frac{a}{1-r}$$ Where $$S$$ is the sum of the series, $$a$$ is the first term, and $$r$$ is the common ratio between terms. In this case, $$a = 3 \times 10^{-1}$$(which is 0.3) and $$r = 10^{-1}$$(which is 0.1). Plugging these values into the formula, we get: $$x = \frac{3 \times 10^{-1}}{1 - 10^{-1}}$$ $$x = \frac{3 \times 10^{-1}}{9 \times 10^{-1}}$$ Simplifying, we find that the fraction representation of $$x$$ is: $$x = \frac{3}{9}$$ $$x = \frac{1}{3}$$

To convert the fraction $$\frac{1}{3}$$ to a percent, we will multiply it by $$100\%$$. Percent simply means "per hundred," so when we multiply by $$100\%$$, we are showing the fraction as a proportion of $$100$$: $$\frac{1}{3} \times 100\% = \frac{100}{3}\%$$ Approximately, the percent representation of the repeating decimal $$0 . \overline{3}$$ is: $$33.33\%$$ So, the repeating decimal $$0 . \overline{3}$$ can be written as approximately $$33.33\%$$.