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

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Answer 1 · 2016-03-20T00:46:39

#-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#