Mathematics: Class 5 — Chapter 8: Weight and Capacity

• Kilogram (kg): Used for heavier objects like a bed ($60\text{ kg}$), a bag of rice ($5\text{ kg}$), or a refrigerator ($50\text{ kg}$).
• Gram (g): Used for lighter objects like a water bottle ($650\text{ g}$) or a small packet of chips.

Weighing scales have dials with markings that indicate weight. It is important to identify the maximum capacity of the scale and the value of each division starting from $0$.

To convert kilograms ($kg$) to grams ($g$), multiply the number of kilograms by $1000$.

• $3\text{ kg} = 3 \times 1000\text{ g} = 3000\text{ g}$
• $3\text{ kg } 500\text{ g} = 3000\text{ g} + 500\text{ g} = 3500\text{ g}$
• $5\text{ kg } 50\text{ g} = 5000\text{ g} + 50\text{ g} = 5050\text{ g}$

To convert grams to kilograms, group the thousands place as kilograms and the remaining as grams.

• $10,760\text{ g} = 10\text{ kg } 760\text{ g}$
• $4,080\text{ g} = 4\text{ kg } 80\text{ g}$

Very light objects, such as medicines, gold ornaments, or tiny insects (like ants), are measured in Milligrams (mg).

$$\text{1 g} = \text{1000 mg}$$

• $5\text{ g} = 5 \times 1000\text{ mg} = 5000\text{ mg}$
• $4\text{ g } 100\text{ mg} = 4000\text{ mg} + 100\text{ mg} = 4100\text{ mg}$

For extremely heavy weights, we use larger units:

• Quintal: $\text{1 quintal} = \text{100 kg}$
• Tonne: $\text{1 tonne} = \text{10 quintals} = \text{1000 kg}$

To compare weights, convert them to the same unit first.

• $1\text{ kg } 600\text{ g}$ ($1600\text{ g}$) $< 1700\text{ g}$
• $10\text{ kg } 35\text{ g}$ ($10035\text{ g}$) $= 10035\text{ g}$

Weights can be added or subtracted by grouping kilograms and grams separately, or by converting the entire quantity into grams.

• Addition Example: $2\text{ kg } 500\text{ g} + 1\text{ kg } 750\text{ g} = 3\text{ kg } 1250\text{ g} = 4\text{ kg } 250\text{ g}$.
• Subtraction Example: $2\text{ kg } 500\text{ g} - 1\text{ kg } 750\text{ g} = 2500\text{ g} - 1750\text{ g} = 750\text{ g}$.

• Multiplication: To find the weight of 4 potato sacks each weighing $10\text{ kg } 500\text{ g}$:
  $$4 \times 10\text{ kg } 500\text{ g} = 40\text{ kg } 2000\text{ g} = 42\text{ kg}$$
• Division: To divide $4\text{ kg } 800\text{ g}$ equally into 4 boxes:
  $$4\text{ kg } 800\text{ g} \div 4 = (4\text{ kg} \div 4) + (800\text{ g} \div 4) = 1\text{ kg } 200\text{ g}$$

• To convert litres to millilitres, multiply by $1000$.
  Example: $3\text{ l } 8\text{ ml} = 3000\text{ ml} + 8\text{ ml} = 3008\text{ ml}$.
• To convert millilitres to litres, group the thousands place as litres.
  Example: $14,075\text{ ml} = 14\text{ l } 75\text{ ml}$.

• Addition: $2\text{ l } 500\text{ ml} + 2\text{ l } 800\text{ ml} = 4\text{ l } 1300\text{ ml} = 5\text{ l } 300\text{ ml}$.
• Subtraction: $9\text{ l} - 5\text{ l } 300\text{ ml} = 8\text{ l } 1000\text{ ml} - 5\text{ l } 300\text{ ml} = 3\text{ l } 700\text{ ml}$.