So I think I made a mistake but I just want to confirm I'm getting this right:
In the example, we had the number $2.3151515…$ and were supposed to convert this number into a fraction.
It was then shown to be equal to the sequence $2.3 + \frac{15}{10^3}+\frac{15}{10^5}+\frac{15}{10^7}$ etc.
As such the common ratio is $r = \frac{1}{100}$
Thus we get the sum of the sequence equalling $(2.3)\frac{1}{1-\frac{1}{100}} = \frac{230}{99}$
The problem is, when I checked my solution $\frac{230}{99}$, it's rougly $2.32323232…$ yet the right solution would actually be $\frac{382}{165}$
Does the problem lie within the simplification of the sequence or am I doing something wrong?
Thanks in advance.
Best Answer
The $2.3$ is not be part of your series. The first term in the series is actually $\dfrac{15}{10^3}$ with the common ratio of $\dfrac1{10^2}$.
Your sum should be $$2.3+\frac{\frac{15}{10^3}}{1-\frac1{10^2}}=\frac{382}{165}$$ as desired.