Question

5. Переведите периодическую дробь в обыкновенную и вычислите: 0,12(3)+0,(6) пж помогите пожалуйста​

Answer 1

Ответ:

Пошаговое объяснение:

$\frac{123-12}{900} +\frac{6}{9} =\frac{111}{900} +\frac{6}{9} =\frac{37}{300} +\frac{200}{300}=\frac{237}{300} =\frac{79}{100} =0,79$

Answer 2

Ответ:

241/300

Пошаговое объяснение:

0,12(3)+0,(6)=241/300

1)0,12(3)=123/900=41/300

2)0,(6)=6/9=2/3

3)41/300+2/3=41/300+200/300=241/300

Answer 3

Для перевода периодической десятичной дроби в обыкновенную, мы можем воспользоваться алгебраическими методами.

1. Обозначим "0,12(3)" как x и "0,(6)" как y.

2. Затем выразим x и y в виде обыкновенных дробей:

   x = 0,12(3) = 0,123333... (безконечное повторение тройки) y = 0,(6) = 0,666666... (безконечное повторение шестерки)

3. Теперь мы можем выразить x и y в виде обыкновенных дробей:

   x = 0,12(3) = 0,123333... = 12/100 + 3/1000 + 3/10000 + ... = (12/100) + (3/1000) * (1 + 1/10 + 1/100 + ...) = (12/100) + (3/1000) * (1 / (1 - 1/10)) = (12/100) + (3/1000) * (10/9) = (12/100) + (1/30) = 12/100 + 1/30 = (12/100) + (10/300) = 12/100 + 1/30 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 + 10/300 = 12/100 +