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Dimensional analysis is a strategy of problem solving where you solve a problem by keeping track of the units of the different components. So if someone said, you have 10g of a material of density 0.5g/ml, what is the volume? You have to convert g to ml. So you set it up:
?ml = 10 g x 1 ml/0.5g
the g units cancel out leaving you the answer in ml.
dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions.
*The dimension of a physical quantity is the combination of the basic physical dimensions (usually length, mass, time, electric current, temperature, amount of substance and luminous intensity)for example, speed has the dimension length per time, and may be measured in meters per second, miles per hour, or other units.
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The dimension of a physical quantity can be expressed as a product of the basic physical dimensions mass, length, time, electric charge, and absolute temperature, represented by sans-serif symbols M, L, T, Q, and Θ, respectively, each raised to a rational power.