Who would win in a fight between decimals and fractions?

Is one better than the other?

Whether you like them or not, decimals are now the most common way to subdivide a number — although fractions are still used in common parlance. When using fractions, we mostly use just the simpler forms like halves, quarters, thirds and sometimes eighths (with the exception of inch fractions and maths equations). In the US (and sometimes in Ireland & the UK), it’s actually quite common to see decimals used in units that are traditionally fraction based — such as pounds, ounces and pints.

Like this delightful looking 4.6 oz tin of Vienna sausages:

Or good ‘ol Jarrito’s 1.58 quart bottle of mango soda:

This begs the question: what if we bit the bullet and actually decimalised customary units? This isn’t anything new. When the USA was a newborn independent state, with no currency and no standardised weights & measures, a certain Mr Thomas Jefferson proposed both a decimalised currency, and a decimalised system of weights & measures. After some opposition, the decimalised dollar was adopted by congress and meant that the US was the first country in the world to have a decimalised currency. As for the weights & measures, things were a little more complicated. The French recently had a revolution of their own, and at the time had a rather shambolic system of weights & measures, with over 250,000 different definitions of units depending on region and usage. The French came up with a new system, which became the metric system, and Jefferson wasn’t too pleased with what they came up with. The metre could only be reproduced in Paris, and Jefferson saw this as excluding other nations. It’s not really clear what ever happened to Jefferson’s decimal measures, seems it just fell by the wayside.

Enough of the history lessons: what would a decimal system based on customary units look like?

This post follows in the same vein as a post from last year, where I looked at redefining customary units using more round metric values. In that post, the units were kept by-and-large the same size as what they currently are — but not decimal. This post describes what a decimalised (or pseudo-decimalised as you’ll see below) version would look like, starting with weights.

## Weight/Mass

Unit | Value | Metric |
---|---|---|

Demi-gram (dg) | — | 0.5 g |

Ounce (oz) | 100 dg | 50 g |

Pound (lb) | 10 oz | 500 g |

Stone (st) | 10 lb | 5 kg |

Ton (t) | 100 st | 500 kg |

The table above sets the pound at exactly 500 g, and is entirely decimal. The smallest unit is a made-up unit called the *demi-gram* (0.5 g). It could also include a hundredweight unit of 10 stone if needed.

The disadvantages of this are that the ton is significantly smaller, and the ounce is maybe a little too big. It would be useful for the ton to be identical to the ‘metric tonne’ (and similar to the customary/imperial ton) for international trade purposes; and it would also be useful for the smallest unit to be exactly 1 gram to keep it in line with ‘pure’ metric usage in science, nutrition information etc. To that end; here is another — decimal*ish* — version:

### The not-so decimal version

Unit | Value | Metric |
---|---|---|

Gram (g) | — | 1 g |

Dram (dr) |
5 g | 5 g |

Ounce (oz) | 10 dr | 50 g |

Pound (lb) | 10 oz | 500 g |

Stone (st) | 10 lb | 5 kg |

Duceweight (dcwt) |
20 st | 100 kg |

Ton (t) | 10 dcwt | 1000 kg |

This version adds two non-decimal units (in bold) in order to make the smallest unit the *gram* (subdivided as you would in the metric system (mg, mcg etc)) and the ton the same as the metric tonne (or megagram). The *duceweight* is a made-up unit, I called it that because it’s about twice the size of the customary hundredweight. I know, I’m really clever like that…

## Length

Unit | Value | Metric |
---|---|---|

Inch (in or “) | — | 2 cm |

Foot (ft or ‘) | 10″ | 20 cm |

Pace | 10′ | 2 m |

Furlong | 100 paces | 200 m |

Mile | 10 furlongs | 2 km |

For length, starting with a 2 cm inch, we work up in tens or hundreds to a mile of around 1 ¼ times the size of the current one. The *pace* is kind-of made up, but it is a unit that has appeared throughout history.

The disadvantages here are that, in a decimal-based system, you only really have space for the yard *or* the foot, not both. It would be useful to have a yard that is the same as the metre, seeing as it’s already almost the same. Also, if the mile could be similar in size to its current form it would mean very little road signage changes. The same goes for the inch; it would be easier to not have to change existing tools, piping etc. To that end; here is another — decimal*ish* — version:

### The not-so decimal version

Unit | Value | Metric |
---|---|---|

Inch (in or “) | — | 25 mm |

Foot (ft or ‘) | 10″ | 25 cm |

Yard (yd) | 4′ | 1 m |

Mile (mi) | 1,600 yd | 1.6 km |

Inches can be divided into one of the following:

- Tenths
- Hundreths
- Thous
- (possibly) Traditional fractions, up to sixteenths

This version is only really decimal up to the foot, but it does give a yard that’s equal to the metre — which would help with conversions. The mile is almost exactly the same as the customary one, you could maybe use 1,500 yards but that would mean signage changes for longer distances. You could also have a furlong of 1 tenth or 1 eighth of a mile.

## Volume

Unit | Value | Metric |
---|---|---|

Minim (min) | — | 0.5 ml |

Fluid Ounce (fl oz) | 100 min | 50 ml |

Pint (pt) | 10 fl oz or 32 cu in | 500 ml |

Gallon (gal) | 10 pt | 5 L |

Bushel (bu) | 10 gal | 50 L |

For volume, we set the gallon to 5 L, with 10 pints of 500 ml etc.

As with the gram, it would be useful if the smallest unit was the same as the smallest (everyday) unit in the metric system, so here is what that might look like:

### The not-so decimal version

Unit | Value | Metric |
---|---|---|

Mill (ml) | — | 1 ml |

Fluid Dram (fl dr) |
5 ml | 5 ml |

Fluid Ounce (fl oz) | 10 fl dr | 50 ml |

Pint (pt) | 10 fl oz (32 cu in) | 500 ml |

Gallon (gal) | 10 pt | 5 L |

Bushel (bu) | 10 gal | 50 L |

Here we have a unit (very imaginatively called the *mill*) set to exactly 1 ml, and the non-decimal *fluid dram* set to 5 ml (or 1 teaspoon).

## Would this have worked?

This is probably all a bit academic at this stage. Although it’s not too late to do something like this now, especially in the US, some time around or before the 1970s would probably have been a better time to consider it. I’m not sure if anything like this was ever proposed beyond Thomas Jefferson’s time, but if it had — it would have had some advantages:

- You could keep the existing units people were used to, while also making trade with other countries easier as the units are either the same size, or very easy to convert.
- Forces people into using the new system. When we converted to metric, and introduced the kilogram (a new word), the pound (the old word) didn’t cease to exist — and is still used today. If we instead just re-used the old word (pound) and changed its definition, it would have been easier to move people on to the new system — especially if the new units were of a similar size to the old ones. It forces people’s hands, using the old definitions would have eventually become awkward and impractical.
- You get the advantages that come with decimals, such as ease of precision.
- If using the ‘decimal-ish’ version, there’s no reason why you couldn’t allow the use of simple fractions also, giving people a bit more variety!

Decimalising and re-defining customary units would be (or would have been…) difficult and confusing at first, but I think could have been an easier conversion in the long run rather than converting to the ‘pure’ metric system. Don’t get me wrong, pure SI units would still be used in some areas like science.

The disadvantage of using decimal is of course its divisibility. Decimals fall on their face when you try to divide them into quarters, eighths, thirds, sixths etc. If you really wanted perfection, you could go and add two more numbers to our numbering system. So for example, we could have two more numbers after 9 — so the twelfth number would be written as *10*. That way you could have numbers that divide into nice round decimals — like 0.3 for ^{1}⁄_{4} or 0.4 for ^{1}⁄_{3}. Doing that would of course be nothing short of catastrophic; despite everyone instantly becoming ‘younger’, you would have planes falling out of the sky, stock markets having a meltdown and the “Ten Green Bottles” song would be that bit longer…