Powers of Ten & Units
Zoom from quarks to galaxies.
The nearest star to Earth (after the Sun) is Proxima Centauri, about 4.24 light-years away. The Earth's diameter is about 12,742 km.
How many Earths, laid side by side, would it take to reach Proxima Centauri?
About 3 billion Earths! Proxima Centauri is ~40 trillion km away. Divided by Earth's 12,742 km diameter: ~3.15 × 10⁹ Earths. Space is staggeringly empty.
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Slide to zoom from atoms to galaxies. Watch the powers of ten change.
N = 10ⁿ
Each step up by 1 in the exponent means the quantity is TEN TIMES bigger. From 10³ to 10⁶ is not 'twice as big' — it's a THOUSAND times bigger.
Modern transistors are ~5 nanometers wide — about 20 atoms across. This is 10⁻⁸ m.
GPS orbits at 20,200 km (~10⁷ m). A timing error of 1 microsecond (10⁻⁶ s) causes a 300 m position error.
The observable universe is ~8.8 × 10²⁶ m across — about 10⁴¹ times the width of a proton.
“Powers of ten aren't just notation — they're the language of the universe. Master them, and you can navigate from quarks to quasars.”
Scale Comparison
Pick any two objects and see how they compare in size.
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Compare an atom to a basketball, then a basketball to the Earth. Notice the ratios are similar!
The universe has a hidden symmetry: you're roughly halfway (in powers of ten) between an atom and a star.