# How/When to Combine units?

by alodia
Tags: combine, how or when, phenomenon, units
 P: 15 1) How and When do you multiply or divide or combine units? 2) Is there an intuitive understanding or experience for every permutation of derived units? example: distance is a natural phenomenon we experience and understand intuitively as space between two points or positions we've denoted the unit of meters to measure distance. ~~~ area is a natural phenomenon we experience and understand intuitively as space on a flat surface we've denoted the unit of meters x meters to measure area. ~~~ volume is a natural phenomenon we experience and understand intuitively as space in our 3D world. we've denoted the unit of meters x meters x meters to measure volume. ~~~ mass is a natural phenomenon we experience and understand intuitively as the amount of stuff that something has. we've denoted the unit of kilograms to measure mass. ~~~ density is a natural phenomenon we experience and understand intuitively as the amount of stuff that's inside* some volume of space. we've denoted the unit of kilograms / (meters x meters x meters) to measure density. *why inside? why not outside? what's governing how we even decide what density is? ~~~~~~~~~~~ what about... meters / kilograms? or... kilograms x kilograms? what would they describe? if anything? so am i correct to conclude that all base units and derived units are put together in such a way as to describe only these phenomenons we intuitively understand and experience because if we didn't understand there's no way to describe it ~~~~~~~~~~~ but then how are 'derived units' DERIVED in the first place? experiments? how? mathematically? how? ~~~~~~~~~~~ thanks for your time to read this and please help me understand! and please provide some examples... and please don't just send me to some link of long articles... thanks again.
 P: 35 They should be derived mathematically.
P: 15
 Quote by yoyo16 They should be derived mathematically.
plz examples

 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,260 How/When to Combine units? Derived units are just that: they have been derived from the application of some mathematical or physical formula, like F = ma. In SI, the unit of force, the newton, is derived from this relation, so a newton is derived from base units of kg-m/s^2 http://en.wikipedia.org/wiki/SI_derived_unit
Thanks
P: 1,948
 Quote by alodia so am i correct to conclude that all base units and derived units are put together in such a way as to describe only these phenomenons we intuitively understand and experience because if we didn't understand there's no way to describe it
No, I don't think that's correct. Intuition will often mislead you. Units are defined based on the algebraic relationship used to define physical quantities.

Density is defined as mass/volume, so its units are by definition kg/m3. whether that jives with some pre-existing intuition is a separate question not relevant to the choice of units