"A Half" Versus "One Half" and Others

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In making this distinction, you choose the way it is transcribed depending on how verbatim you want to be. When "eighteen and one half" is said, then it is a mixed number, and the rule says that mixed numbers should be transcribed in figures.

...It is 18 1/2 feet long.

When "three and three fourths" is said, then this mixed number is in figures.

...We need 3 3/4 cups of sugar.

The "issue" arises when "a half" is said or "three quarters" is said. "A" and "quarters" are not really numbers. So for those who want to be "verbatim," these numbers must be written out in their entirety.

...It is eighteen and a half feet long.
...We need three and three quarters cups of sugar.

This format is never correct.

...72 and a half...

Happy punctuating!