Question

Представить в виде обыкновенной бесконечную десятичную дробь 0(153)

Answer 1

0,(153) = 0,153153153... = 1*10^(-1) + 5*10^(-2) + 3*10^(-3) + 1*10^(-4) + 5*10^(-5) + 3*10^(-6) + 1*10^(-7) + 5*10^(-8) + 3*10^(-9) + ... = 100*10^(-3) + 50*10^(-3) + 3*10^(-3) + 100*10^(-6) + 50*10^(-6) + 3*10^(-6) + 100*10^(-9) + 50*10^(-9) + 3*10^(-9) + ... = 153*10^(-3) + 153*10^(-6) + 153*10^(-9) + ... = 153*(10^(-3) + 10^(-6) + 10^(-9) + ...) = 153*10^(-3)*(1 + 10^(-3) + 10^(-6) + ...) = 153*10^(-3)*["геометрическая прогрессия: 1-й член = 1, q = 10^(-3)"] = 153*10^(-3)*[1/(1 - 10^(-3))] = (153/1000)*[1000/(1000 - 1)] = 153/999

 

Ответ: 0,(153) = 153/999

Answer 2

Representing 0.(153) as an Infinite Decimal Fraction

To represent the decimal fraction 0.(153) as an infinite decimal, we can follow the pattern of the repeating digits and place a bar over them. The number 0.(153) can be written as 0.153153153....

This means that the digits 1, 5, and 3 repeat infinitely. To indicate this, we place a bar over the repeating digits: 0.153̅.

So, the infinite decimal representation of 0.(153) is 0.153̅.

Please note that this representation assumes that the pattern of repeating digits continues indefinitely.