Consider the standard unit of length: meter. How was it divided into decimeter, centimeter, millimeter, etc. when there were no shorter lengths than the standard? What is the physical/experimental process involved?
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3$\begingroup$ What do you mean? Take a meter, cut it in ten and you get ten decimeters. $\endgroup$– jinaweeCommented Jan 12, 2014 at 9:25
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$\begingroup$ @jinawee I think he means physically. I'd say you just "do your best" and make small adjustments until it seems about right. $\endgroup$– Brandon EnrightCommented Jan 12, 2014 at 9:27
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2$\begingroup$ My guess is that originally compass-and-straightedge tricks were used. $\endgroup$– Brandon EnrightCommented Jan 12, 2014 at 9:30
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3$\begingroup$ @jinawee You want to cut it in ten equal pieces, that is more delicate than just ten pieces. $\endgroup$– BernhardCommented Jan 12, 2014 at 10:23
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2$\begingroup$ The OP should really consider fleshing out this question some more, to better facilitate a more targeted response. The yearly publications from the NIST on measurement standards is a testimony to just how much can be written on the subject if a person is of a mindset to do so. $\endgroup$– David HCommented Jan 12, 2014 at 11:23
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1 Answer
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Well historically people were using all sorts of accurate and inaccurate units, remember there were times when measurements were done in arm length, foot length etc. So absolutely there were both smaller and larger units before the establishment of any system.
For another part of your question, if you were given a meter rod and told to make a new unit $0.25 m$ I guess you would cut an equal length of cloth or paper and fold it as accurately as you can once and then again so as to make 4 fragments as equal as possible and then your task would be done, a new unit would be formed. Historically people were fiddling over unit systems such as mks, cgs, fps etc, but once the most established system i.e. the SI was established the decimal system was also widely accepted (it may be that decimal system was adopted before SI system, sorry if thats the case) anyway so we performed similar experiments by folding to make 10 fragments or joining 10 fragments and we got milli,centi, deci,deca,kilo,mega etc
answered Jan 12, 2014 at 17:22