On a recent chapter test covering probability, I gave an extra credit question of this type: 850!/848! . For those who are questioning what's so exciting about the numbers 850 and 848, the exclamation points indicate a mathematical operation known as "factorial". Factorial means to multiply all the whole numbers from 1 to whatever number you're looking at, so 850! means 850*849*848*...*3*2*1 and 848! means 848*847*846*...*3*2*1. And yes, I allowed the students to use calculators.
Math people can easily see why I chose these particular numbers. Unless someone has some ultra powerful calculator, the number 850! is too large for most calculators to handle.
This is one of those times where I get to see who thinks and who pushes buttons, who uses the calculator as a tool and who uses it as a crutch.
All the numbers in the fraction 850!/848! cancel except for 850*849 in the numerator, which gives an answer of 721,650.
One student listed the answer as "Overflow Error". There's an error, all right, but it isn't in the calculator's limited memory capacity!
Update: Interestingly enough, the calculator built into MS Windows handled the computation just fine, despite the answer's involving 10 to the 2,122nd power.