It would be more accurate to say that calculating with very large integers or integer fractions with millions of digits can be slow on current computers - but it's still far beyond what humans can typically do without assistance.

Million-digit numbers are absurdly large in terms of physical quantities, but can easily arise when one is enumerating possibilities, such as the number of ways that one could give out randomized phone numbers to everyone in a city.

(That's the sort of explanation that my mathematically-inclined friends and I would have understood in grades 3-5, when we learned about integers, rational and irrational numbers, and basic probability/combinatorics, as well as simple algorithms for multi-digit arithmetic and conversion between integer and decimal fractions.)

Factorial and exponential functions were (and are) fun to play with on calculators because of the large numbers you can generate; python and mathematica are even more fun of course. I think recent TI and Casio graphing calculators support python, though I don't know about their bignum support or memory limits.