π and e Approximations

Using standard approximations for π (≈ 3.1) and e (≈ 2.7) can lead to several other useful values for estimation problems (which typically have a ±5% margin of error).

• π² ≈ 10
• e³ ≈ 20
• πe ≈ 8.5
• e² ≈ 7.4

Knowing these allows you to quickly approximate more complex expressions. For example, $(e \times \pi)^4 = e^4 \times \pi^4 = e \cdot e^3 \cdot (\pi^2)^2 \approx 2.7 \times 20 \times 10^2 = 5400$.