Truncation and round-off errors
General · Mathematics
Study notes
Q: Approximate e^0.1 by 1+x+x²/2. Bound truncation and round-off errors. e^0.1 ≈ 1+0.1+0.005 = 1.105. Truncation: |R₂| ≤ e^0.1(0.1)³/6 ≈ 1.105×0.001/6 ≈ 1.8×10⁻⁴. Round-off (3 decimals): ~0.5×10⁻³ = 5×10⁻⁴. Total ≈ 7×10⁻⁴. True: 1.10517: error 1.7×10⁻⁴ ✓! (Two error sources!)