The near-base multiplication trick — what determines the "base," and which numbers is it best for?

The base is the nearby round number (10, 100, 1000); the method shines when both factors are close to it.

Numbers hug a base so their deviations are small and easy to multiply. Near 100, 97×94 and 103×104 are trivial; near 1000, 998×997 works the same way (deviations −2, −3 → 995 | 006 → 995006). The further a number sits from the base, the larger the deviation product becomes and the less the trick helps — then fall back to the cross method.