Guides
A profile answers what a number is. These answer the questions that are about the relationship between numbers, which no single profile can carry.
Powers of two, and why computers are full of them
“why does computing use powers of two”
Why 256, 1024 and 65,536 turn up everywhere in computing, what a bit width actually limits, and why the storage on a disk never matches the number on the box.
Exact and approximate numbers
“what is the difference between an exact and an approximate number”
Why the speed of light has no error bar and the mass of the Earth does, what it means for a constant to be defined rather than measured, and how to read a figure that has been rounded.
Million, billion, trillion
“what is the difference between a million and a billion”
How much bigger a billion really is, why the word once meant two different amounts, and the clearest way to feel the gap between the three.
Binary and hexadecimal
“how do binary and hexadecimal work”
Why computers count in twos, why programmers write in sixteens, and how to read a hex colour or a memory address without converting anything in your head.
Orders of magnitude
“how do you compare very large and very small numbers”
Why the exponent matters more than the digits in front of it, how scientific notation makes unlike quantities comparable, and what an order of magnitude actually buys you.
Why sixty seconds, sixty minutes, twenty-four hours
“why are there 60 seconds in a minute”
Why time is the last place we still count in sixties, where the twenty-four-hour day came from, and why nobody has managed to decimalise either.