Question

Как перевести 0.0(3) в обыкновенную дробь?

Answer 1

а)

x = 0.0(3) = 0.03333333...

10x = 0.(3) = 0.3333333...

10x - x = 9x = 0.3

x = 0.3/9 = 1/30

б)

0.0(3) = 0.03 * 1.(1) = 0.03(1 + 0.1 + 0.1^2 + 0.1^3 + ...) = 0.03 * 1/(1 - 0.1) = 0.03/0.9 = 1/30