🔢 Numerical Practice:
Conversions & Derived Quantities
Sharpen your skills with these numerical problems on unit conversions and derived quantities. Try them yourself, then check your answers below!
📝 Practice Problems
- Convert 5.2 km into metres and centimetres.
- Convert 2 500 g into kilograms and milligrams.
- A rectangular sheet is 2.5 m long and 1.2 m wide. Find its area in m² and cm².
- A cube has side length 12 cm. Calculate its volume in cm³ and m³.
- A mass of 450 g occupies 0.0005 m³. Determine its density in kg/m³.
✅ Worked-Out Solutions
1. Converting 5.2 km
1 km = 1000 m ⇒ 5.2 km = 5.2 × 1000 = 5200 m
1 m = 100 cm ⇒ 5200 m = 5200 × 100 = 520 000 cm
2. Converting 2 500 g
1 kg = 1000 g ⇒ 2500 g = 2500 ÷ 1000 = 2.5 kg
1 g = 1000 mg ⇒ 2500 g = 2500 × 1000 = 2 500 000 mg
3. Area of Rectangular Sheet
Area = length × width = 2.5 m × 1.2 m = 3.0 m²
1 m² = (100 cm)² = 10 000 cm² ⇒ 3.0 m² = 3.0 × 10 000 = 30 000 cm²
4. Volume of Cube
Volume = side³ = (12 cm)³ = 12 × 12 × 12 = 1728 cm³
1 m³ = (100 cm)³ = 1 000 000 cm³ ⇒ 1728 cm³ = 1728 ÷ 1 000 000 = 0.001728 m³
5. Density Calculation
Mass = 450 g = 450 ÷ 1000 = 0.45 kg
Density = mass ÷ volume = 0.45 kg ÷ 0.0005 m³ = 900 kg/m³
