More accuracy from analog multiplication?
From a bit more information in the comments, you are using an ATMega168. This microcontroller has three options for the ADC reference voltage:


\$V_\mathrm{CC}\$ - usually 5 or 3.3 V.
Internal 1.1 V bandgap reference
External reference (&lt; \$V_\mathrm{CC}\$)


With the 10bit ADC, you then split this into \$2^{10}\$ bins (LSB). To avoid the need to prescale your signal in order to use the maximum dynamic range of the ADC, you can also select a more appropriate reference.

In your case, the internal 1.1 V reference gives LSBs of ~1.1 mV and is very easy to use. Simply set ADMUX[7:6] = b11 and put a capacitor on the AREF pin. If you want to use an external 1.024 V reference, this gives LSBs of 1.0 mV; set ADMUX[7:6] = b00. 

Another advantage of using the bandgap or an external reference is that you are not directly using the noisy \$V_\mathrm{CC}\$ rail as your reference voltage. Typical reference ICs will include lots of filtering, and will give you the lowest noise of the options.