Scientific Notation & SI Units
Grades 7+ Teens & adults Science
The universe is rude about scale. The sun's mass is a 2 followed by thirty zeros; an atom's width starts with eleven zeros after the decimal point. Nobody wants to count those zeros — so science invented a shorthand: write the important digits, then multiply by a power of ten.
The pattern
- Positive exponent → big number: 10⁶ = a million.
- Negative exponent → small number: 10⁻³ = a thousandth.
- To convert: count how many places the decimal point moved — that count is the exponent.
Why it's worth learning
Multiplying huge numbers becomes adding exponents: (2×10⁸)(3×10⁶) = 6×10¹⁴. Comparing scale becomes instant: 10⁸ beats 10⁵ by a thousand-fold, no counting zeros. It's the same "biggest place value first" instinct as our left-to-right methods — lead with the digits that matter.
SI units — the agreed measuring sticks
Science only works if everyone measures the same way. The International System of Units (SI) defines seven base units — meter, kilogram, second, ampere, kelvin, mole, candela — and prefixes in powers of ten: kilo (10³), milli (10⁻³), nano (10⁻⁹). Scientific notation and SI prefixes are the same idea at two scales.
- BIPM (2019). The International System of Units (SI Brochure), 9th edition. Bureau International des Poids et Mesures. bipm.org/en/publications/si-brochure — the definitive, free definition of every SI unit.
- Thompson, A., & Taylor, B. N. (2008). Guide for the Use of the International System of Units (NIST Special Publication 811). National Institute of Standards and Technology. nist.gov/pml/special-publication-811 — the US companion guide with every conversion rule.
- Write 45,000 in scientific notation (4.5 × 10⁴)
- Write 0.0072 (7.2 × 10⁻³)
- Earth is ~1.5×10¹¹ m from the sun — how many km? (1.5×10⁸ km)
Next: measurement & precision — how honest scientists report numbers · estimation.