# Different determinant for same matrix

I have the following matrix: $$A=\begin{bmatrix} 2883,4675 & 44263,069125 & 724401,86824027 \\ 44263,069125 & 724401,86824027 & 12346864,4095603\\ 724401,86824027 & 12346864,4095603 & 216427597,203037 \end{bmatrix}$$ And I want to calculate the determinant. I know of two ways I can do this. Either I use the rule of Sarrus or I split the matrix (Laplace expansion) and calculate it this way.

Using the rule of Sarrus would give us: $$det(A)=2883,4675\cdot724401,86824027\cdot216427597,203037+44263,069125\cdot12346864,4095603\cdot724401,86824027+724401,86824027\cdot44263,069125\cdot12346864,4095603-724401,86824027^{3}-44263,069125^{2}\cdot216427597,203037-2883,4675\cdot12346864,4095603^{2}$$

I calculated the determinant using Excel and got exactly $$122305571810432$$

Splitting the matrix gives us: $$\begin{bmatrix} 2883,4675\begin{vmatrix} 724401,86824027 & 12346864,4095603\\ 12346864,4095603 & 216427597,203037 \end{vmatrix}\\ -44263,069125\begin{vmatrix} 44263,069125 & 12346864,4095603\\ 724401,86824027 & 216427597,203037 \end{vmatrix}\\ +724401,86824027\begin{vmatrix} 44263,069125 & 724401,86824027\\ 724401,86824027 & 12346864,4095603 \end{vmatrix} \end{bmatrix}$$ Which leads to: $$det(A)=2883,4675(724401,86824027\cdot216427597,203037-12346864,4095603\cdot12346864,4095603)-44263,069125(44263,069125\cdot216427597,203037-12346864,4095603\cdot724401,86824027)+724401,86824027(44263,069125\cdot12346864,4095603-724401,86824027^{2})$$ Calculating that value in Excel gives me $$122305571810516$$

I tried using a few websites which allowed me to calculate the determinant online, I got different results again. One gave me $$122305571810432,17$$ And the other one gave me $$122305571810440$$

Why is it that I'm getting a different determinant for the same matrix? Is one method more accurate than another? Or maybe there is a different method which I did not try and is even more accurate?

Picture from the excel table

Formula for B1:=A3*A5*A7+A4*A6*A5+A5*A4*A6-A5^3-A4^2*A7-A3*A6^2
Formula for B2:=A3*(A5*A7-A6^2)-A4*(A4*A7-A6*A5)+A5*(A4*A6-A5^2)

To see an example of (part of) what is happening, take your number $122305571810432$ in your Excel cell, and now in another cell add $0.3$ to it, and look at the result.