I consider dimensional analysis a basic concept that all chemists (and professionals in general) should have in their pocket. The ability to perform rapid problem-solving and unit conversions is, without question, an essential skill in the lab.

 For example:

Since all these quantities represent the same physical quantity, they can be written as:

But also as:

Since the numerator and denominator represent the same physical quantity, the fraction is equivalent to 1 and can be rewritten in either order (numerator or denominator).

These fractions are called conversion factors. To make calculations, we choose the conversion factors that cancel units each other, depending on the specific need.

Let's analyze the data we have:

Assuming the baseball team has 24 players. This calculation can be resolved in just one line, using dimensional analysis:

What about applied to Chemistry. 

This reaction is used to convert alcohols into alkyl halides.
Suppose you need about 1.2–1.5 molar equivalents of iodine. How many milligrams of iodine correspond to 1.5 equivalents, if you start with 1.5 g of alcohol (compound 4)?

Using dimensional analysis, this can be solved in a single line of multiplication:

Let's calculate this:

How many atoms are in 25.1 g of sulfur?
If your calculation gives 4.71 × 10²³ atoms, you now see how dimensional analysis can be used to solve problems ✅

References:

(1) https://www.nist.gov/pml/owm/metric-si/unit-conversion
(2) Chang, Raymond; Goldsby, Kenneth. General Chemistry: The Essential Concepts (p. 19). McGraw-Hill Higher Education.