Scientific Calculations Using Arithmetic
Science is built on arithmetic. Every physical formula you encounter — whether in physics, chemistry, or biology — comes down to the four operations applied to measured quantities.
Key Scientific Formulas
| Formula | Variables |
|---|---|
| Speed = Distance ÷ Time | v = d/t |
| Density = Mass ÷ Volume | ρ = m/V |
| Pressure = Force ÷ Area | P = F/A |
| Power = Energy ÷ Time | P = E/t |
| Frequency = 1 ÷ Period | f = 1/T |
Worked Examples
Speed
A car travels 240 km in 3 hours. Speed = 240 ÷ 3 = 80 km/h
Density
A stone has mass 150 g and volume 60 cm³. Density = 150 ÷ 60 = 2.5 g/cm³
Standard Form (Scientific Notation)
Very large or very small numbers are written as a × 10ⁿ where 1 ≤ a < 10.
3,400,000 = 3.4 × 10⁶ 0.000056 = 5.6 × 10⁻⁵
Key Takeaways
- Every scientific formula uses arithmetic to relate measured quantities.
- Always include units in your answer.
- Standard form handles very large and very small numbers cleanly.
- Rearranging a formula is just applying inverse operations.
Practice Questions
- Calculate the speed of a train that covers 540 km in 4.5 hours.
- An object has mass 350 g and volume 140 cm³. Find its density.
- A machine uses 4,500 J of energy in 30 seconds. Find its power in watts.
- Write 0.0000072 in standard form.
- Calculate the distance covered at 55 m/s for 12 seconds.