What is the collector current of this transistor circuit?
You say you want precise numbers (I think you mean accurate) and you are not willing to assume that \$I_B \ll I_C\$. At this point you should use a good SPICE simulator instead of hand calculations. However, the model parameters for the transistor will also be approximations so those results won't be 100% accurate either.

You could build the circuit and test it, as long as all of your test equipment is under calibration and traceable to NIST. However, there is a great deal of variation between transistors of the same part number, so your results will only be valid for that one single transistor and those particular four resistors. If you build another copy of the circuit you will get different results.

We are engineers here. Make the assumption about \$I_B\$ and get along with the project.