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Convert the following. Show working to gain full marks2 marks each Convert 5.6 km to metres Convert 2500 mL to Liters Convert 3.5 hours to seconds Convert 7 800m to kilometres Convert 2.4 kg to grams Convert 25 days to seconds

Mathematics

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Here are the solutions to your questions.

Section A: Basic Conversions

  1. Convert 5.6 km5.6 \text{ km} to metres.
  1. Recall the conversion factor for kilometers to meters.

    $$
    1 \text{ km} = 1000 \text{ m}
    $$
    
  2. Multiply the given value by the conversion factor.

    $$
    5.6 \text{ km} \times 1000 \frac{\text{m}}{\text{km}} = 5600 \text{ m}
    $$
    The converted value is $\boxed{\textbf{5600 m}}$.
    

    2. Convert 2500 mL2500 \text{ mL} to Liters.

  3. Recall the conversion factor for milliliters to liters.

    $$
    1 \text{ L} = 1000 \text{ mL}
    $$
    
  4. Divide the given value by the conversion factor.

    $$
    2500 \text{ mL} \div 1000 \frac{\text{mL}}{\text{L}} = 2.5 \text{ L}
    $$
    The converted value is $\boxed{\textbf{2.5 L}}$.
    

    3. Convert 3.5 hours3.5 \text{ hours} to seconds.

  5. Recall the conversion factors for hours to minutes and minutes to seconds.

    $$
    1 \text{ hour} = 60 \text{ minutes}
    $$
    $$
    1 \text{ minute} = 60 \text{ seconds}
    $$
    
  6. Multiply the given hours by the conversion factors.

    $$
    3.5 \text{ hours} \times 60 \frac{\text{minutes}}{\text{hour}} \times 60 \frac{\text{seconds}}{\text{minute}} = 12600 \text{ seconds}
    $$
    The converted value is $\boxed{\textbf{12600 seconds}}$.
    

    4. Convert 7800 m7800 \text{ m} to kilometres.

  7. Recall the conversion factor for meters to kilometers.

    $$
    1 \text{ km} = 1000 \text{ m}
    $$
    
  8. Divide the given value by the conversion factor.

    $$
    7800 \text{ m} \div 1000 \frac{\text{m}}{\text{km}} = 7.8 \text{ km}
    $$
    The converted value is $\boxed{\textbf{7.8 km}}$.
    

    5. Convert 2.4 kg2.4 \text{ kg} to grams.

  9. Recall the conversion factor for kilograms to grams.

    $$
    1 \text{ kg} = 1000 \text{ g}
    $$
    
  10. Multiply the given value by the conversion factor.

    $$
    2.4 \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 2400 \text{ g}
    $$
    The converted value is $\boxed{\textbf{2400 g}}$.
    

    6. Convert 25 days25 \text{ days} to seconds.

  11. Recall the conversion factors for days to hours, hours to minutes, and minutes to seconds.

    $$
    1 \text{ day} = 24 \text{ hours}
    $$
    $$
    1 \text{ hour} = 60 \text{ minutes}
    $$
    $$
    1 \text{ minute} = 60 \text{ seconds}
    $$
    
  12. Multiply the given days by the conversion factors.

    $$
    25 \text{ days} \times 24 \frac{\text{hours}}{\text{day}} \times 60 \frac{\text{minutes}}{\text{hour}} \times 60 \frac{\text{seconds}}{\text{minute}} = 2160000 \text{ seconds}
    $$
    The converted value is $\boxed{\textbf{2160000 seconds}}$.
    

    Section B: Area & Volume

    1. A classroom is 8 m8 \text{ m} long and 5 m5 \text{ m} wide. Find the area in cm2\text{cm}^2.
  13. Convert the length and width from meters to centimeters.

    $$
    1 \text{ m} = 100 \text{ cm}
    $$
    $$
    \text{Length} = 8 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 800 \text{ cm}
    $$
    $$
    \text{Width} = 5 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 500 \text{ cm}
    $$
    
  14. Calculate the area using the formula for the area of a rectangle.

    $$
    \text{Area} = \text{Length} \times \text{Width}
    $$
    $$
    \text{Area} = 800 \text{ cm} \times 500 \text{ cm} = 400000 \text{ cm}^2
    $$
    The area of the classroom is $\boxed{\textbf{400000 cm}^2}$.
    

    2. A water tank holds 0.75 m30.75 \text{ m}^3 of water. Convert this to Liters. Hint: 1 m3=1000 L1 \text{ m}^3 = 1000 \text{ L}.

  15. Use the given conversion factor for cubic meters to liters.

    $$
    1 \text{ m}^3 = 1000 \text{ L}
    $$
    
  16. Multiply the given volume by the conversion factor.

    $$
    0.75 \text{ m}^3 \times 1000 \frac{\text{L}}{\text{m}^3} = 750 \text{ L}
    $$
    The volume in Liters is $\boxed{\textbf{750 L}}$.
    
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