What is a Fermi estimate (order-of-magnitude reasoning)?

Break an impossible-looking quantity into a chain of rough factors you can each guess to the nearest power of ten, then multiply — errors tend to cancel.

Classic: how many piano tuners in a city of 1,000,000? Chain it: ~250,000 households × (1 piano per ~20 households) × (1 tuning/year) ÷ (~1,000 tunings per tuner/year) ≈ ~12 tuners.

Each factor might be off, but over- and under-estimates partly cancel, so the magnitude (tens, not thousands) is usually right. Fermi estimates answer "roughly how big?" — perfect for judging whether a figure is even plausible.