Five foot nine is not 5.9 feet

Five foot nine is 5.75 feet, because nine inches is three quarters of a foot. Writing it as 5.9 adds nearly two inches. It is exactly the same error as reading 7.45 decimal hours as seven hours forty-five minutes — a base-twelve quantity being read as if the fractional part were decimal.

Both go wrong in the same direction and for the same reason, and both are avoided by dividing by the base rather than by ten.

How does the conversion actually run?

Centimetres to inches first, then split the inches into feet and a remainder. 175 cm is 68.9 inches; 68.9 ÷ 12 is 5 with 8.9 left over, so 5 feet 8.9 inches — usually rounded to 5 foot 9.

Note that 183 cm lands on exactly six feet, which is why that figure appears so often as a threshold — it is a round number in one system and a coincidence in the other.

Why is a common size not a common measurement?

Because a great deal of imperial usage is a label rather than a dimension, which the nominal sizes article covers for timber and screens. Ounces have the same problem in the other direction.

One ounce is exactly 28.349523125 grams, because the pound is defined as exactly 0.45359237 kg and an ounce is a sixteenth of it. Cooking rounds it to 28, which is within 1.2 per cent and fine for a recipe.

The ounce you almost certainly want is avoirdupois. A troy ounce, used for precious metals, is 31.10 grams — about 10 per cent heavier — and a fluid ounce is a volume that has no fixed relationship to either.

Do spoons convert cleanly?

The ratio holds even though the absolute sizes do not. Three teaspoons make a tablespoon in the US, in the UK and under the metric convention, so any recipe written in spoons scales internally without conversion.

Australia is the exception, and it is the one that bites. An Australian tablespoon is 20 ml, so it takes four teaspoons rather than three — which means an Australian recipe calling for two tablespoons of a strong ingredient is asking for a third more than a British or American cook would give it.

The absolute sizes differ too: a US tablespoon is about 14.8 ml, a metric one exactly 15, and a UK one 15 by convention. Those differences are within measurement error for most cooking and the ratio break is not.

Why does Roman numeral conversion need rules rather than a factor?

Because it is not a positional system. Two rules do most of the work: a smaller symbol before a larger one subtracts, so IV is four and IX is nine; and only I, X and C can be used subtractively, which is why 99 is XCIX rather than IC.

Standard subtractive form is what a converter should produce — 4 is IV rather than IIII, even though clock faces traditionally use the latter. Malformed input is better rejected than guessed at, because IIII and IC both have a plausible intended value and no correct one.

There is no zero and no way to write one, which is the structural limitation that makes the system unusable for arithmetic and perfectly adequate for labelling a chapter.

Where else does the base change?

In three places people meet regularly and rarely think about. Angles run in sixty minutes to a degree and sixty seconds to a minute, so 40.5 degrees is 40°30′ rather than 40°50′. Latitude and longitude inherit that directly, which is why a coordinate written as a decimal and one written in degrees-minutes-seconds look nothing alike.

And printing runs in twelves: twelve points to a pica, which survives in typography as the reason point sizes behave the way they do. None of the three announces its base, and all three produce the same class of error when read as decimal.

What is the general defence?

Ask what the base is before dividing. Feet are twelve inches, hours are sixty minutes, a pound is sixteen ounces, a stone is fourteen pounds. None of them is ten, and every one of them is written with a decimal point somewhere it does not belong.

The related habit is to convert once, at the end, rather than through a chain. Each step rounds, and the rounding article covers what happens when several of them compound.

Questions people ask

How do I write a height properly? Feet and inches with the primes — 5′ 9″ — or centimetres. The decimal-feet form is technically valid and almost always misread.

Is 28 grams close enough for an ounce? For cooking, comfortably. For anything sold by weight, the exact figure of 28.349523125 is a definition rather than an approximation and is worth using.

Why is a stone fourteen pounds? Historical trade standardisation, and it survives in the UK almost exclusively for body weight. It is the reason a UK weight is often three numbers rather than one.

Do any converters get the ratio wrong? Spoon converters that assume a 15 ml tablespoon everywhere will be wrong by a third on Australian recipes. It is worth checking which convention a tool uses.

Divide by the base the unit actually uses. The height converter handles the feet-and-inches split, ounces to grams uses the exact definition, tablespoon to teaspoon covers the ratio and its one exception, and the Roman numeral converter is the case where there is no base at all.