For the record, I mostly work in Decimal Inches, to three places. That is, 1.000"; thousandths of an inch. That's because I grew up in the US metalworking/machine shop/mechanical engineering industry in the '70's and '80's. That's what I'm familiar with. Metric/SI moved into the US industry in the '80's. By the '90's, almost all US industry works in Metric/SI.
I learned to work Metric/SI in my jobs as a mechanical engineer from the mid-80's on. But in my own shop, I still like to work with Decimal Inches, because most of my machines and tools are from that era of 1900 to 1980. US machinery and measuring tools pre-1980 were almost all in "thousandths". The scales and graduations and feed threads are in Thousandths.
In common (old time) machine shop talk, numbers are spoken in thousandths. For example 1.562" is pronounced "one point five six two". And 1.560" is pronounced "one point five six zero", not "one point five six". And 1.500" is "one point five zero zero". You say the three digits to indicate that you are working to measurements of three places; 0.001", "a thousandth".
If you are working to four or more places, then you say the extra digits; 1.5623" is "one point five six two three". That extra fourth digit is called "a tenth". It means one ten-thousandth of an inch. When an old machinist says the part needs to be "two tenths over", that means +0.0002". Not +0.2"
If the dimension is equal to a fraction, then it's acceptable to call it a fraction. 1.5625" can be called "one and nine sixteenths". But that implies a lower tolerance level. If a machinist calls for a hole to be drilled with a 1 9/16" drill bit, that assumes that the hole will end up at as much as 1/16" oversize. That's a roughing hole, which will then be bored or reamed to a more precise size in thousandths.
That's the common language for old-time US metalworking and machine shop work.
Now, US woodworking shops, like cabinet shops and boatyards, usually work in Fractional Inches. Even today, most rulers and tape measures at a US Home Depot are in Fractional Inches. It's still the most popular measurement system for woodworking in the US, although Metric/SI is slowly catching on.
The smallest unit of measurement in Fractional Inches is usually 1/64", called "a sixty fourth". For example, 1 3/8" is spoken "one and three eighths" and 1 5/64" is spoken "one and five sixty-fourths". Occasionally, you'll hear reference to "a twenty-eighth" which is 1/128" or one half of 1/64". A cabinetmaker may call for a part to be cut "a twenty-eighth over", which means half a sixty-forth oversize. Woodworking language. To translate, a "sixty-forth" is about equal to "fifteen thousandths". That's how machinists and cabinetmakers speak to each other.
There's also some confusing things about the Metric/SI system. SI (Systems Internationale) is not the same as the classic European Metric or Asian (Japanese) Metric systems. SI was developed in the '70's as a worldwide compromise between the US Decimal Inches system and the various classic Metric systems. It was pretty well accepted in US industry by the 1990's. Europe took a little longer. SI units are mostly in 3-place intervals, like the Decimal Inches system. Dimensions are called out in Kilometers, Meters and Millimeters.