what Is the recurrIng decImal 2.1666666666... converted to a fractIon?

Answer 1

To convert the recurring decimal ( 2.166666...) to a fraction, let ( x = 2.166666...). We can separate the whole number and the decimal part, expressing it as ( x = 2 + 0.166666...). The decimal ( 0.166666...) can be written as ( \frac{1}{6}), since it is equal to ( \frac{1}{6} = 0.166666...). Therefore, combining these, ( x = 2 + \frac{1}{6} = \frac{12}{6} + \frac{1}{6} = \frac{13}{6} ). Thus, ( 2.166666... = \frac{13}{6} ).