analogReference(INTERNAL) not seeming to "rescale" millivolt input

I am trying to use analogReference(INTERNAL); to reference small millivolt inputs. When I monitor the results in the serial monitor, they do not appear to be any different than when i don't include the analogReference statement.
My (possibly wrong) assumption is that without he statement included in the "set-up" that an analog input is a 5volt input is ADC converted to a 1024 result. Therefore, 1VDC input would result in a display of aprox. 204. A 500 mV input would result in a display of 100.

When inserting the "analogReference(INTERNAL) in to the "set up" I was expecting to see the 1024 now being referenced to aprox. 1.1 volt.
Therefore 1volt DC input would display slightly less than1024 and a 500 mV input would indicate aprox. slightly less than 512.

No matter what I include the displayed output always seems to be "scaled" 5volts/1024.

I am using two different UNO's.
One is an older original version one and has the ATMEGA328P-PU
The other is a Rev3 and has the ATMEGA328P U

I am using a 1.5 volt battery and a 5K ohm pot as a voltage source for my input.
(I will try and and attach a photo of my configuration.)
I have the negative of battery wired to one end of pot and to UNO ground.
I have the positive of battery wired to opposite end of pot.
The "wiper" of pot is wired to analog input A3.

I am going to attempt to attach my sketch and a drawing of my wiring to the UNO.

I haven't done a post in a long time so I apologize for any incorrect things that I have done.

I would greatly appreciate it if participants could explain my misconception and/or my errors that may be in my code.

I will attempt to attach code and drawing.

And I Thank you for your patience, understanding, and help.
Rick

[code]


#include <SD.h>

File myFile;

void setup() {
  // put your setup code here, to run once:

  Serial.begin(9600);
  pinMode(10, OUTPUT);

  if (!SD.begin(10)) {
    Serial.println("initialization failed!");
    return;
  }

  analogReference(INTERNAL);

}

void loop() {
  // put your main code here, to run repeatedly:

  float raw = analogRead (A3);
  delay (500);
  raw = analogRead (A3);

  float calc = raw * 5.0725;

  Serial.print (raw);
  Serial.print ("   ");
  Serial.println (calc, 3);

  myFile = SD.open("ricks.txt", FILE_WRITE);
  myFile.println (calc, 3);
  myFile.close();

  delay (5000);

}
[/code]

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