1. **Problem 3.1.1:** Write 2,7 million in full using numerals only. 2,7 million means 2.7 million, which is 2.7 × 1,000,000. Calculate: $$2.7 \times 1,000,000 = 2,700,000$$ **Answer:** 2,700,000 2. **Problem 3.1.2:** Determine the total mass of the carp caught by Andrew and Duncan in kg. Andrew's carp mass: 2.375 kg Duncan's carp masses: 1.2 kg and 750 g Convert 750 g to kg: $$750 \text{ g} = \frac{750}{1000} = 0.75 \text{ kg}$$ Total mass caught by Duncan: $$1.2 + 0.75 = 1.95 \text{ kg}$$ Total mass caught by both: $$2.375 + 1.95 = 4.325 \text{ kg}$$ **Answer:** 4.325 kg 3. **Problem 3.2.1:** Calculate the total volume of all holes dug for the 12 posts in cubic meters. Each hole is a square prism with side length 30 cm and depth 60 cm. Convert cm to meters: $$30 \text{ cm} = 0.3 \text{ m}, \quad 60 \text{ cm} = 0.6 \text{ m}$$ Volume of one hole: $$V = \text{length} \times \text{width} \times \text{depth} = 0.3 \times 0.3 \times 0.6 = 0.054 \text{ m}^3$$ Total volume for 12 holes: $$12 \times 0.054 = 0.648 \text{ m}^3$$ **Answer:** 0.648 m³ 4. **Problem 3.2.2:** Explain why Andrew had some concrete left over after planting all posts. When mixing concrete, some volume is lost due to: - Concrete settling and compacting in the holes, reducing volume needed. - Spillage or leftover concrete from mixing more than exact volume. - Posts displace some volume inside the holes, so less concrete is needed than the hole volume. Therefore, mixing exactly the hole volume results in leftover concrete. 5. **Problem 3.2.3:** Calculate the mass of river sand needed to make 1 m³ of concrete. Given: - 0.75 m³ concrete requires 5.5 bags of cement. - Cement : River Sand : Stone ratio = 1 bag : 2 wheelbarrows : 2 wheelbarrows. - One wheelbarrow of river sand weighs 102 kg. Step 1: Find number of cement bags per 1 m³ concrete: $$\frac{5.5 \text{ bags}}{0.75 \text{ m}^3} = \frac{5.5}{0.75} = 7.3333 \text{ bags/m}^3$$ Step 2: River sand per 1 bag cement is 2 wheelbarrows. So river sand per 1 m³ concrete: $$7.3333 \times 2 = 14.6667 \text{ wheelbarrows}$$ Step 3: Convert wheelbarrows to kg: $$14.6667 \times 102 = 1496.0 \text{ kg}$$ **Answer:** Approximately 1496 kg of river sand is needed for 1 m³ of concrete.