1. The problem involves comparing decimal numbers, ordering them, and writing inequalities or equalities between pairs of decimals. 2. Important rules: - To compare decimals, align the decimal points and compare digits from left to right. - If digits differ at any place, the number with the smaller digit is smaller. - Trailing zeros after the decimal point do not change the value (e.g., 6.1 = 6.10). - When ordering numbers, list them from smallest to largest. 3. Write the smallest decimal number from each pair: a) 34.91 (only one number) b) 24.92 (smaller than 311.67) c) 6.12 (smaller than 6.9) d) 6593 (only one number) e) 631 (smaller than 724) f) 5.41 (smaller than 5.6) g) 25.67 (smaller than 25.76) h) 301.8 (only one number) i) 0.049 (smaller than 0.05) 4. Write the correct inequality between each pair: a) 2.05 < 2.24 b) 8.35 > 2.81 c) 7.6 > 7.099 d) 18.05 < 18.06 e) 3.04 > 3.01 f) 2.78 < 2.785 g) 0.072 > 0.02 h) 28.882 < 28.88 5. Write the correct sign (= or ≠) between each pair: a) 6.1 = 6.10 b) 2.99 ≠ 2.9 c) 5.995 ≠ 5.994 d) 4.406 = 4.406 e) 87.0 = 87 f) 0.0075 ≠ 0.0076 6. Order the decimal numbers from smallest to largest: a) 2.56, 4.41, 4.46, 4.49 b) 0.52, 0.59, 0.71, 0.77 c) 6.06, 6.9, 6.92, 6.97 d) 5.199, 5.2, 5.212, 5.219 e) 42.4, 42.42, 42.44, 42.49 f) 9.04, 9.09, 9.39, 9.7, 9.901, 9.99 7. Challenge: Write measurements in order from smallest to largest (convert all to same units): a) 60 mm = 6 cm, 8.15 cm, 0.081 m = 8.1 cm; order: 6 cm, 8.1 cm, 8.15 cm b) 0.00672 t = 6.72 kg, 6.750 g = 0.00675 kg, 6.7 kg; order: 0.00675 kg, 6.7 kg, 6.72 kg c) 0.00347 km = 3.47 m, 3455 mm = 3.455 m, 3.48 m, 346 cm = 3.46 m; order: 3.455 m, 3.46 m, 3.47 m, 3.48 m 8. Zack's decimal cards: [6.46], [6.47], [6.48] a) Possible numbers for middle card: 6.470, 6.471, 6.479 b) Number of different numbers with three decimal places between 6.470 and 6.479 is 10 (from 6.470 to 6.479 inclusive) c) Check by counting from 6.470 to 6.479 in increments of 0.001 9. Order the following numbers: 2110 ÷ 100 = 21.10 0.0298 × 100 = 2.98 1.9 × 10⁻³ = 0.0019 2.30 × 10⁻⁴ = 0.00023 10⁻² = 0.01 Order: 0.00023, 0.0019, 0.01, 2.98, 21.10 Final answers are given above with detailed explanations for each step.