Dividing by 2pi on a scientific calculator?

You need to be aware of what exactly is in the numerator and denominator, and then type the values into the calculator accordingly.

For the fraction 1/2pi, you will get different answers if pi is being multiplied by 1/2 vs. 1 being divided by 2pi.

For the former, type (1/2)pi and you will get 1.5708.  This is equivalent to pi/2.  For the latter, type 1/(2pi) and you will get 0.15916.  This needs to be cleared up before you bring in the decimal.

Once you bring in 1.2661, you must make it clear to the calculator where this decimal is located in the fraction.  If you have (1/2)*(pi*1.2661), you will get 1.9888.  This is equivalent to (pi*1.2661)/2.  However, if you have 1/(2*pi*1.2661) you will get 0.1257.

Get into the habit of using parentheses to be on the safe side.  If you forget to specify what exactly is in the numerator or denominator, your calculation will likely be off.

Thank you so much for this insightful answer, Amin. I could not for the life of me understand why I kept getting a different (and incorrect) answer on my ti-84. You cleared it right up, though. The calculator was computing 365/2 * π rather than 365/2π. Inputting the correct parentheses solved the problem. Much obliged!