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Units and Measurement
Question
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Can a quantity have units but still be dimensionless? Give examples.

Answer

Yes, there are certain quantities which have units but they are dimensionless. 
For example, angle, loudness, solid angle. 

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Some More Questions From Units and Measurement Chapter

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?