Everyday Maths
The mental arithmetic that saves you money in a shop, a showroom or a meeting.
Every portable or window AC listing leads with a BTU number. Here's the rule of thumb behind it, worked by hand, and where to add a safety margin.
Every comfortable staircase is built around one number: a riser height close to 7.5 inches. Here's how that single target turns a total rise into a step count, an exact riser height, and a run length — worked by hand.
"Drink eight glasses a day" ignores that a 60 kg adult and a 100 kg adult don't need the same amount. A single per-kilogram multiplier gets you a number scaled to you.
A CPU spec, a radio dial and a spinning hard drive all measure frequency, but in units separated by factors of a thousand — or by a completely different unit, RPM, that still reduces to the same hertz.
A food label, a physics textbook and an electricity bill all measure the same thing — energy — in three different units. One multiplication gets you between any of them.
Car engines, microwaves and air conditioners all measure power — the rate energy moves — but in three incompatible units. Here's the arithmetic that connects them.
Computers count in base 2 and programmers shorthand it in base 16 — the divide-and-remainder method gets you between any two bases by hand.
Roman numerals aren't positional like decimal digits — they're built from seven symbols and a subtraction rule, and that rule is the whole trick.
Your ISP sells speed in bits per second; your download bar shows bytes per second. One division by 8 explains the gap.
Drive makers count in decimal terabytes; your operating system counts in binary tebibytes. Neither number is wrong — they're just not the same unit.
Tire gauges, weather reports and dive tables all use different pressure units — one multiplication through pascals connects any two of them.
Every time unit is a fixed multiple of one second — the only decision is which multiple, and the only risk is a definition of "year" nobody agreed on.