Simplify coefficients on symbolic fraction

Hello, I will get right into it with an example:

I have this symbolic fraction:

 (360107496127452805861054873600*z + 425427235801022494957005157967)/(60847228810955011271841753858048*z^2 - 156454140823163360723132970172416*z + 100320120403779201256199576503770)

As you can see it has pretty big coefficients. Simplifying it should get something like this:

 0.0059182*(z+1.181)/((z-1.221)*(z-1.35))

Is there any simple way to get to this result? I've been messing with simplify(), collect() and such, but got nothing.

Thank you in advance.

Answer 1

[John D'Errico]

Did you try vpa? Yeah, I suppose the name might not be obvious.

syms z

vpa((360107496127452805861054873600*z + 425427235801022494957005157967)/(60847228810955011271841753858048*z^2 - 156454140823163360723132970172416*z + 100320120403779201256199576503770),5)

ans =
(3.6011e29*z + 4.2543e29)/(6.0847e31*z^2 - 1.5645e32*z + 1.0032e32)