Question

Запишите в виде дроби десятичное периодическое число 17,02(36)

Answer 1

Пусть х = 0,023636..., тогда
100х = 2,3636...
10000х = 236,3636...
Уравнение: 10000х - 100х = 236 - 2
                     9900х = 234
                     х = 234/9900 
                     х = 13/550 - сократили на 18
Ответ: 17,02(36) = 17 целых 13/550.
                      

Answer 2

Answer:

The decimal periodic number 17,02(36) can be expressed as a fraction as follows:

17,02(36) = 17 02/100 + 36/9900

Let's break it down:

1. 17,02(36) = 17 02/100 - The whole number part is 17. - The decimal part is 02, which can be expressed as 02/100.

2. 17,02(36) = 17 02/100 + 36/9900 - The repeating part is 36, which can be expressed as 36/99, since there are two digits in the repeating part. - To convert 36/99 to a fraction with a denominator of 100, we multiply both the numerator and denominator by 100, resulting in 3600/9900.

Therefore, 17,02(36) = 17 02/100 + 36/9900.

This breakdown allows us to express the decimal periodic number 17,02(36) as a fraction.