Chapter 11
Estimation & Calculation Shortcuts
Rounding, digit analysis, approximation techniques
11.1 Strategic rounding
Round to the nearest convenient number, then compute
Example: 623 × 0.317 ≈ 600 × 0.3 = 180. Exact: 197.5. The estimate correctly identifies the answer as 'about 200' and rules out 20 or 2 000.
11.2 Sum first, then round
Total cost share = sum all percentages Remaining share = 100% − Total cost share
Example: costs 31.4% + 14.8% + 11.6% = 57.8% ≈ 58%. Remaining ≈ 42%. On €5 200 000 → ≈ €2 184 000.
11.3 Bounding — ruling out impossible options
Lower bound: round all factors down Upper bound: round all factors up
Example: (318 × 47) − (124 × 53). Lower ≈ 6 350. Upper ≈ 10 000. Exact = 8 374. An answer of 20 000 is immediately eliminated.
11.4 Units digit analysis
Units digit of (A × B × C) = units digit of (units_A × units_B × units_C)
Example: units digit of 463 × 729 × 581? Units digits: 3, 9, 1. 3×9=27 → 7. 7×1=7. Answer ends in 7.