Математика18 мин
Standard and Compound Units
Convert between SI units and reason about compound rates (speed, density, pressure) without losing track of the units.
01
SI prefixes and conversions
All SI prefixes are powers of 10. Memorise the ladder once and conversions become arithmetic.
| Prefix | Symbol | Power of 10 |
|---|---|---|
| kilo | k | 10³ |
| hecto | h | 10² |
| deca | da | 10¹ |
| base | — | 10⁰ |
| deci | d | 10⁻¹ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
Going up the ladder (smaller → larger) the number gets smaller. Going down, bigger. Check direction before multiplying.
02
Compound rates
Speed conversion
A car travels at 90 km/h. Convert to m/s.
- Divide by 3.6: .
- Or expand: .
Жауап: 25 m/s
03
Area, volume and pitfalls
- Area scales by the **square** of the linear factor: 1 m² = 10000 cm².
- Volume by the **cube**: 1 m³ = 10⁶ cm³.
- Don't multiply when you should divide: 30 km at 60 km/h takes ½ h, not 60·30.
Жаттығу
A block has mass 240 g and volume 60 cm³. What is its density in g/cm³?
Жауап пен түсініктемені көру
Жауап: 4 g/cm³
g/cm³.