I am trying to put in row reduced echelon form the following matrix
$$
\left(
\begin{array}{ccc}
 -0.1 & 0.1 & 2 \\
 0.3 & 0.2 & 0.7 \\
 0 & 0.5 & 6.7 \\
\end{array}
\right)
$$
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, 0.7}, {0, 0.5, 6.7}}]

```

which agrees with my result. I also tried in [WolframAlpha](https://www.wolframalpha.com/input/?i=RowReduce%5B%7B%7B-0.1,+0.1,+2%7D,+%7B0.3,+0.2,+0.7%7D,+%7B0,+0.5,+6.7%7D%7D%5D), 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](https://www.wolframalpha.com/input/?i=RowReduce%5B%7B%7B-1%2F10,+1%2F10,+2%7D,+%7B3%2F10,+2%2F10,+7%2F10%7D,+%7B0,+5%2F10,+67%2F10%7D%7D%5D) 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.