Avogadro's number, electron charge, distance to stars — none of them fit neatly on a page. Scientific notation makes them readable.
This used to be a back-of-the-envelope job. Now it is one tap, but the logic has not changed. Avogadro's number, electron charge, distance to stars — none of them fit neatly on a page. Scientific notation makes them readable.
Coefficient (1 ≤ |x| < 10) × 10^exponent. 6.02 × 10²³ — that's 602 sextillion.
1.6 × 10⁻¹⁹ = very small (electron charge in coulombs).
Multiply coefficients, add exponents. (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹.
Numbers with more than ~6 zeros either side of the decimal. Engineering, chemistry, finance, astronomy.
Why isn't 12 × 10³ valid scientific notation? Coefficient must be 1–10. Use 1.2 × 10⁴ instead.
How does my calculator display it? Usually 6.02E23 or 6.02 × 10^23, depending on model.
Whatever number you land on, sanity-check it against a second method or a quick estimate in your head.