Scientific Notation to SI Units — Complete Guide
How to convert scientific notation to SI units
Engineering calculations frequently produce values in scientific notation combined with non-SI units — for example 1.427 × 10⁷ mm³. Converting these correctly to SI base units requires understanding both the scientific notation and the SI prefix system.
What is scientific notation?
Scientific notation expresses numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. It avoids writing long strings of zeros and makes very large or very small numbers easier to read and compare.
Examples: 14,270,000 = 1.427 × 10⁷ | 0.00000427 = 4.27 × 10⁻⁶
SI prefix table
| Symbol | Name | Factor | Example |
|---|---|---|---|
| T | tera | 10¹² | 1 THz = 10¹² Hz |
| G | giga | 10⁹ | 1 GN = 10⁹ N |
| M | mega | 10⁶ | 1 MPa = 10⁶ Pa |
| k | kilo | 10³ | 1 km = 10³ m |
| — | (base) | 10⁰ | m, Pa, kg, N |
| m | milli | 10⁻³ | 1 mm = 10⁻³ m |
| μ | micro | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| n | nano | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| p | pico | 10⁻¹² | 1 pF = 10⁻¹² F |
The conversion method
To convert A × 10ⁿ [prefix][unit] to SI base units, follow these four steps:
- Look up the prefix exponent p (e.g. milli → p = −3)
- If the unit has a dimensional power d (e.g. mm³ → d = 3), the prefix contributes p × d to the exponent
- Add: total exponent = n + (p × d)
- Result = A × 10(n + p×d) [base unit]d
Cubed units: mm³ → m³
The most common mistake in unit conversion is forgetting to apply the dimensional power to the prefix. When converting mm³ to m³, the prefix (milli = 10⁻³) must be cubed:
mm = 10⁻³ m → mm³ = (10⁻³)³ m³ = 10⁻⁹ m³
= 1.427 × 10⁷ × 10⁻⁹ m³
= 1.427 × 10⁽⁷⁺⁽⁻⁹⁾⁾ m³
= 1.427 × 10⁻² m³
= 0.01427 m³
More worked examples
3.5 × 10⁴ kN → N
= 3.5 × 10⁴ × 10³ N = 3.5 × 10⁷ N = 35,000,000 N
250 μPa → Pa
= 250 × 10⁻⁶ Pa = 2.5 × 10⁻⁴ Pa = 0.00025 Pa
6.2 × 10³ cm² → m²
= 6.2 × 10³ × 10⁻⁴ m² = 6.2 × 10⁻¹ m² = 0.62 m²