I keep trying to do 2574/2598960 for my statistics homework, and it gives me the answer in scientific notation rather than in the decimal form. My settings are currently Normal, Float, Auto, Real, Radian. I've messed around with various modes and am unable to get it out of scientific notation.
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You are correct in that your mode should be one of "Normal", "Scientific" or "Engineering".  Both Engineering and Scientific display answers with an exponent.  According to the TI-84 manual, "Normal" mode uses up to 10 digits in the answer with the decimal point somewhere in the middle.  However, there is this note:

Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI-84 expresses the answer in scientific notation.

You will notice that the input "2574/2598960" gives the result "9.903961585E-4".

But "2574/259896" gives the result ".0099039616", which is what you expect.

The simple answer is to write the answer down and move the decimal point 4 digits to the left and leave off the exponent.

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