How do you convert -3.09 (09 repeating) to a fraction?

Question

4262 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-20T00:46:39

$- \frac{34}{11}$ $-34/11$

take $x=-3.090909.....$

If you calculate 100x you will have -309.090909

Now calculate:

$100x-x=-309.090909+3.090909=-306$

$99x=-306$

$x=-306/99$

Both denominator and numerator are multiple of 9 so we can simplify, by dividing both by 9:

$x=-34/11$