Lithium button cells, often called coin cells, are designated by their diameter and thickness in millimeters and tenths of millimeters, i.e. CR2032.

The proposal is that coins in circulation should be of regular sizes, i.e. 10mm diameter x 1mm thickness, 15mm diameter x 2mm thickness, this information
being marked on the coin.

This would provide anyone with a handful of change with immediate access to a useful, reproducible measurement standard.

I like to tell people that the reason that a '99 (a type of
ice-cream piped into a polystyrene cone from a criminal
in an ice-cream-van and topped with a crumbly bit of
chocolate) is so-called because the flakey chocolate,
otherwise known as a "flake" is always exactly 99mm long
and that the naming coincided exactly with both
decimalisation and Margaret Thatcher (who invented
whippy ice-cream of this nature prior to going on a
crusade against flare-wearing hippies and other
nerrdowells)*

* It should be noted that a proportion of the earlier
statement, somewhere between 0 and 1, is utter
bollocks.

Likewise a sheet of A0 paper is exactly 1m² - so A1 is
œm², A2 is Œm², A3 is 1/8m², A4 is 1/16m², and so on.
When we start
using 'A' paper sizes as currency things will all get a
lot easier.

...and so it follows that a sheet of 80gsm A3 paper
weighs 10g (and this
is easier to carry around than 2 litres of water,
although I suppose you can drink the water if you're
thirsty)

Some coin facts I've found: 16 pennies stacked equals 1 inch and 16 pennies in a line equals 1 foot. 5 quarters weigh an ounce. A 1 yen coin weighs 1 gram, and has a radius of 1cm.