Orders of magnitude
You almost never need the exact number; you need to know whether it is plausible. An adult weighs on the order of a hundred kilos, not ten and not a thousand; a car moves at tens of metres per second, not thousands. That habit — round to the nearest power of ten and compare — is what catches a calculation error without redoing it, and what lets you argue about energy bills or distances with no data in front of you. Here you sort four things by mass, by speed or by energy, and the hard part is not the extremes: it is the two in the middle.
Where this sits
- Opens up
- The scale
Exercises from this rung
Generated by the app, from easiest to hardest
Sort them from lightest to heaviest
Answer an atom, a bacterium, a red blood cell, a car
Why an atom: 10⁻²⁶ kg · a bacterium: 10⁻¹⁵ kg · a red blood cell: 10⁻¹³ kg · a car: 1.4 × 10³ kg
easierSort them from slowest to fastest
Answer a snail, an ant, a cat, sound in air
Why a snail: 10⁻³ m/s · an ant: 3.0 × 10⁻² m/s · a cat: 1.3 × 10¹ m/s · sound in air: 3.4 × 10² m/s
in betweenSort them from smallest to largest
Answer the width of DNA, a hair's width, a cat, a marathon
Why the width of DNA: 2.0 × 10⁻⁹ m · a hair's width: 7.0 × 10⁻⁵ m · a cat: 5.0 × 10⁻¹ m · a marathon: 4.2 × 10⁴ m
harder