What is a chain?
The chain is a surveying unit of 66 feet, which is exactly 20.1168 meters. It is divided into 100 links of 7.92 inches each, and 80 chains make a mile.
The chain was devised by the English mathematician Edmund Gunter around 1620 and used to survey land. Ten square chains make exactly an acre, which is why surveyors liked it. GPS has replaced it for most work, though US public land surveys are still recorded in chains and links.
What is a microinch?
A microinch (µin) is the inch with the SI prefix micro, meaning one millionth, so 1,000,000µin make one inch.
The microinch is mostly seen in surface finish. US drawings give a part's roughness (Ra) in microinches, and a typical machined finish is 63µin, or 1.6µm.
A microinch is a millionth of an inch, which is exactly 0.0254 micrometers or 25.4 nanometers. Outside the US surface finish is given in micrometers instead.