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Can a quantity have units but still dimensionless? Can a quantity have dimensions but still unitless?

A quantity cannot have units until it has dimensions.

A quantity that has dimensions must have units.

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Yes a quantity have units but still be dimensionless for example,unit of angle is radian ,but it is a dimensionless quantity.

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A dimensionless quantity can have a unit there are many examples for it ....radian and other in chem this is clearly written in hc verma part 1
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yes
you can cosider angle, solid angle
which have units but are dimensionless quantities
 
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A dimensionless quantity may have unit. Eg. angle has a unit degree or radian but it has no dimension. A unitless quantity never has a non-zero dimension.
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A dimensionless quantity may have unit. Eg. angle has a unit degree or radian but it has no dimension. A unitless quantity never has a non-zero dimension. And So A Quantity may have unit but no dimension
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yes
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yessss
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