Because important decisions are often made on the basis of measurements.
Would you like your doctor to diagnose your illness on the basis of a very rough measure of you pulse / blood pressure / etc. Would you like your builder to build a house on approximate vertical angles? Or your car to be designed on rough calculations?
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The article at the link below should help you get a handle on the subtle differences between accuracy and precision.
when one scientist tells another scientist that something is certain length, that measurement should mean the some thing to both of them.
yes
Your measurement should include one estimated digit.
FR or F is the common abbreviation for the diameter measurement French