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# [JavaScript (Node.js)], 242 bytes

```javascript
s=>([l,p,i,j,_,r]=/(-)?\+?(\d*)\.?(\d*?)((((\d+)\7|\d)(?=\.))|$)/.exec(s),r=r||'0',[i,r]=c(c([i|0,1],[j|0,10**(l=j.length)]),[r,10**l*(10**r.length-1)]),[(p?-i:i)/(j=d(i,r)),r/j])
c=(a,b)=>[a[0]*b[1]+b[0]*a[1],a[1]*b[1]]
d=(a,b)=>b?d(b,a%b):a
```

[Try it online!][TIO-ktj69bfo]


Regexes are love, regexes are life.

## Explanation

The meat of it is this regex here: 

```
/(-)?\+?(\d*)\.?(\d*?)((((\d+)\7|\d)(?=\.))|$)/
```
In order:

 1. `/(-)?\+?` Captures the optional negative or positive sign (we don't actually care about the positive sign, so it is outside the group.

 2. `(\d*)` Capture the integer part, if any

 3. `\.?` Optional period

 4. `(\d*?)` Captures the non-repeating decimal part

 5. `((((\d+)\7|\d)(?=\.))|$)` The complicated one. Captures either: 

    - `(\d+)\7` A repeating part of the decimal followed by a period `(?=\.)`
    - `\d` The last digit followed by a period `(?=\.)`
    - Nothing, we've reached the end of the string (`$`) and there is no period, meaning there is no repeating part

Once that's done it's a relatively simple formula to get the fraction. We just add together the integer part, the decimal part, and the fractional part as fractions, for which we have a helper method `c` which takes two fractions and outputs their sum as a (non-reduced) fraction:

<p>$$
\frac{i}{1}+\frac{j}{10^{\text{#digits of }j}}+\frac{r}{10^{\text{#digits of }j}\cdot(10^{\text{#digits of }r}-1)}
$$</p>

Finally, we have a helper method `d` which computes the greatest common divisor using Euclid's method. We divide by this to reduce the fraction, and at the same time multiply the numerator by whatever the sign was to get the final answer.

[JavaScript (Node.js)]: https://nodejs.org
[TIO-ktj69bfo]: https://tio.run/##pVLNbuIwGDyTp7AQW2ywjZ0EaFoZTrsv0GMSbUNi2qCoQU521RXk2akd8gN0Vz1sDrG/me@bGVveRb@jIlbpviRveSJPW3EqxAr6Gd7jFO/wT6xCMYMErYPpGgbJBAW0XtcI6i9IpihYHoMEwbUIKELHEZpR@S5jWCCshDoex2yM/dTIxDCGfnpkmIfY35mVTSYwEzuaybeX8hWFCPuqRrMJNItqGMJrDu7XJH1I0QzuRAK1JtIes12IrFjACG@QWPmRz8LJxufhdGN2kd5h86ux0Eraxs06gRscfdugh@gU529FCUpZlAUQwLcG/pANMfBN1BCbktzUU0ZvENc2tWv3LTXQ12RharLoAfusQfoeds/nBtJLh9Eb55ua3NT0U9JPUQmtoxGO5w3iUO4aiM@XeM5aJYfSWpxjpzPnvAO9BuSUdVhrYVOvwZz@cJTb3TTzsMfYJWM3lIsd5wrn/yLsXowbtS64pi5Y28ae53XXc8V5zSS7pltLvTOzLUu47bjzBTWL4zY9ZME5Z8t7zrHrmcuzwkfL2uYKwP5dgXx7fl8IHKzBGS9KpV@bQfVLfWxR@b6XcSmTluKGKtUfM9e0bFUUa3oLtQLSXoNBugXQoFoICCE6EVPf3dUDWuia4mGd5SyaZ5Jm@Qt8fvoVx7IoHsDoAMfDMZjWMadA7xHdR8lTGakScgeDMRijCpCV7mysKzBrCx5WzzraYFABmRXyL0Y/ojSTyVc@7tc@AHZXNjpcHPzcdXHcCjWRLJ0qjsr4FUqlUHex/xHtu1K5qtUrqzp9AA "JavaScript (Node.js) – Try It Online"