I am trying to put in row reduced echelon form the following matrix $ $ \left( \begin{array}{ccc} -0.1 & 0.1 & 2 \ 0.3 & 0.2 & 0 \ 0 & 0.5 & 6.7 \ \end{array} \right) $ $ I did the calculations by hand, and being a fairly simple matrix to reduce, I wanted to test it out in Mathematica, using

RowReduce[{{-0.1, 0.1, 2}, {0.3, 0.2, 0}, {0, 0.5, 6.7}}] 

which agrees with my result. I also tried in WolframAlpha, keeping the same input, however, I get an “incorrect result”, which is $ $ \left( \begin{array}{ccc} 1 & 0. & 0. \ 0 & 1 & 0. \ 0 & 0 & 1 \ \end{array} \right) $ $ I noticed that there is a dot next to some of the $ 0$ s, so I am assuming there are some rounding errors being made. So I tried this and it worked.

My question is, why is mathematica able to work with greater precision than Wolfram Alpha, even though the function being called is the same?

I am aware that this question does not involve solely Mathematica, however since the function is the same for both I wanted to understand the how each handled this.