# Module 4 Day 8 C3

• The hint is a bit confusing because the question only has four 1s, and the hint says the number is equal to 0.25+0.00111111...+0.0000001111. From the question, I thought the number was 0.251111222222222222222222222222222222222222222.... $$\text{\tiny{you get the idea}}$$, but I think the hint is saying that the number is 0.2511111111111111111111111....

• @divinedolphin You were right to initially think that the decimal was $$0.251111\overline{2222}\ldots.$$ The multiple $$2$$'s come from the overlap of the first set of $$1$$'s in $$0.\textcolor{blue}{00}\overline{\textcolor{red}{1111}111111}\ldots$$ plus the second set of $$1$$'s in $$0.\textcolor{blue}{00}\textcolor{red}{0000}\overline{1111}\ldots$$

The first set of $$1$$'s is shifted over to the right by two spaces, allowing the $$25$$ to appear.
The second set of $$1$$'s is shifted to the right by $$6$$ spaces, allowing the four $$\textcolor{red}{\text{red } 1}$$'s from the $$0.\textcolor{blue}{00}\overline{\textcolor{red}{1111}111111}\ldots$$ to show through.
And the remaining $$2$$'s come from the places that have $$1$$'s in both the $$0.\textcolor{blue}{00}\overline{\textcolor{red}{1111}111111}\ldots$$ and the $$0.\textcolor{blue}{00}\textcolor{red}{0000}\overline{1111}\ldots$$ .