Accepting that the VBE of most small signal silicon transistors falls within the range 0.6 to 0.8v under normal operating conditions and that hfe lies between 50 and 1000
if i want to build a single stage amplifier running off 5v DC with a nominal collector current of 100uA. a) What would be the value of RE that would ensure that there was less than 10% error in IC.
You also must consider the current in the voltage divider that provides the base current so that a transistor with a low hFE does not drag down the base voltage too low.
Your collector current is so low that the base-emitter voltage for a 2N3904 transistor is typically 0.6V and could be lower. Look at the graph in its datasheet.
Your range of Vbe is too much. Some transistors have a low Vbe and others have a high Vbe. they all have a voltage range so select one transistor part number then its voltage range will be from maybe 0.55V to 0.65V at a collector current of only 100uA.
The biasing error can be reduced by adding more negative feedback by changing the upper divider resistor to the collector instead of to the positive supply, but then the input impedance and gain are reduced.