Use a geometric series to find the rational number represented by the repeating decimal. 1.123...

Question

Trigonometry homework that I do not understand

Answer 1

1.123123123123.... = 1 + 0.123 + 0.000123 + 0.000000123 + ...

Ignoring the 1, we have a geometric series with first term 0.123 and common ratio 0.001.

The sum of the series is 0.123 / [ 1- 0.001] = 123 / 999

So, 1.123123123... = 1 + 123 / 999 = 1122 / 999 = 374 / 333