Question

Выяснить какую из дробей 24/5, 3/11, 14/9, 3/32 можно представить в виде бесконечной периодической десятичной дроби период которой равен 5

Answer 1

14/9 делим, получаем 1,55555...

Answer 2

Ответ: 14/9 = 1,(5555555)

Answer 3

Представление дробей в виде бесконечной периодической десятичной дроби

Из предоставленных дробей 24/5, 3/11, 14/9, 3/32, давайте выясним, какую из них можно представить в виде бесконечной периодической десятичной дроби, период которой равен 5.

24/5: 24 divided by 5 equals 4.8, which can be represented as a finite decimal. Therefore, 24/5 cannot be represented as an infinite periodic decimal with a period of 5 [[8]](https://files.sch2000.ru/pdf/lessons/math/metod_6kl.pdf).

3/11: 3 divided by 11 equals 0.272727..., where the period is 27. Therefore, 3/11 can be represented as an infinite periodic decimal with a period of 27, not 5.

14/9: 14 divided by 9 equals 1.555..., which can be represented as a finite decimal. Therefore, 14/9 cannot be represented as an infinite periodic decimal with a period of 5.

3/32: 3 divided by 32 equals 0.09375, which can be represented as a finite decimal. Therefore, 3/32 cannot be represented as an infinite periodic decimal with a period of 5.

Based on this analysis, the only fraction that can be represented in the form of an infinite periodic decimal with a period of 5 is 3/11.