The metric system is deliberately designed to be simple arithmetically yet capable of _______ expansion as it becomes necessary to __________ new units of measure.

The metric system needs to be able to grow endlessly as science advances. 'Indefinite' means unlimited or without end - perfect for a system that must keep expanding. 'Invent' matches creating new units when needed. The other options don't fit: confusing (contradicts 'simple'), mathematical (doesn't imply expansion), rigid (opposite of flexible), limited (contradicts the need for growth), record/discard/correct don't match creating new measurements.