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The degree of unsaturation (U), or index of hydrogen deficiency (IHD), is defined as the difference in the number of pairs of hydrogen atoms between the compound and the acyclic alkane with the same number of carbon atoms. Each double bond or ring costs two hydrogen atoms compared to a saturated analog and results in one degree of unsaturation.
The degree of unsaturation for hydrocarbons is U = (2C + 2 − H) / 2, where C is the number of carbon atoms and H is the number of hydrogen atoms.
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Just like β-keto acids—which upon thermal decarboxylation form ketones—β-dicarboxylic acids undergo decarboxylation to generate monocarboxylic acids with the liberation of carbon dioxide.

Malonic ester synthesis is a method to obtain α substituted carboxylic acids from ꞵ-diesters such as diethyl malonate and alkyl halides.