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Posted by Frank Taylor on December 8, 2015 (updated February 25, 2017)
The plural of most English nouns is formed simply by adding an -s or -es to the end, but words that were borrowed from Latin and other languages “present some of the most troublesome aspects of English plurals.” For nouns that end with -um, the appropriate form of the plural is sometimes the Latin -α and sometimes the English -ums.
The examples include the English nouns “forum,” “dictum,” “datum,” and “memorandum.” How can we determine which form of the plural to select? As a “reliable guide,” the third edition of Garner’s Modern American Usage recommends, “if in doubt, use the native-English plural ending in -s.”
“For general matters of spelling,” the sixteenth edition of The Chicago Manual of Style relies on its preferred dictionaries, “Webster’s Third New International Dictionary and the latest edition of its chief abridgment, Merriam-Webster’s Collegiate Dictionary.” In Chapter Seven, The Chicago Manual explains its practice with regard to the selection of a plural:
Where Webster’s gives two forms of the plural — whether as primary and secondary variants, like zeros and zeroes, or as equal variants, like millennia and millenniums — Chicago normally opts for the first. In some cases, however, different forms of the plural are used for different purposes. A book may have two indexes and a mathematical expression two indices, as indicated in the Webster’s entry for index.
Another manual of style may recommend a different practice. For us as writers, the important points are to be alert for instances in which we need to choose between two forms of a plural and to maintain a consistent practice for making these choices.
 “Most nouns form their plurals simply by adding -s. … But if a word ends with the sound of –s-, -sh-, -ch-, or -z-, the plural is formed by adding -es.” Bryan A. Garner, Garner’s Modern American Usage, 3rd ed. (New York: Oxford University Press, 2009), s.v. “plurals … A. Generally.”
 “Words imported into the English language from other languages — especially Greek, Latin, French, and Italian — present some of the most troublesome aspects of English plurals. Many imported words become thoroughly naturalized; if so, they take an English plural. But if a word of Latin or Greek origin is relatively rare in English — or if the foreign plural became established in English long ago — then it typically takes its foreign plural.” Garner’s Modern American Usage, s.v. “plurals … B. Borrowed Words.”
 “The Latin plural being -α, and the English -ums, three selections follow of nouns (1) that now always use -ums, either as having completed their naturalization, or for special reasons; (2) that show no signs at present of conversion, but always use -α; (3) that vacillate, sometimes with a differentiation of meaning, sometimes in harmony with the style of writing, and sometimes unaccountably.” H.W. Fowler and R.W. Burchfield, eds., Fowler’s Modern English Usage, rev. ed. (New York: Oxford University Press, 2004), s.v. “-um.”
 Garner’s Modern American Usage, s.v. “plurals … B. Borrowed Words.”
 The Chicago Manual of Style, 16th ed. (Chicago: University of Chicago Press, 2010), 7.1.
 The Chicago Manual of Style, 7.6.
 In relevant part, Garner defines the term “inflection” as “[t]he change of form that a word undergoes to distinguish its case, gender, mood, number, voice, or other characteristics. … Nouns are inflected to show that they are plural.” Bryan A. Garner, “Glossary of Grammatical, Rhetorical, and Other Language-Related Terms,” in Garner’s Modern American Usage, 900.
 We might find inflectional information “[i]n individual dictionary entries,” under cross-references, or “as outside matter.” Bo Svensén, A Handbook of Lexicography: The Theory and Practice of Dictionary-Making (Cambridge: Cambridge University Press, 2009), 126, 129. In this context, the term “outside matter” refers to the components of a dictionary other than “the ordered set of dictionary entries.” Svensén, A Handbook of Lexicography, 76.
I found this explanation under the “Help” section of Merriam-Webster Online:
The plurals of nouns are shown in this dictionary when suffixation brings about a change of final -y to -i-, when the noun ends in a consonant plus -o, when the noun ends in -oo or -ey, when the noun has an irregular plural or a zero plural or a foreign plural, when the noun is a compound that pluralizes any element but the last, when a final consonant is doubled, when the noun has variant plurals, and when it is believed that the dictionary user might have reasonable doubts about the spelling of the plural or when the plural is spelled in a way contrary to expectations.
“Explanatory Notes to the Dictionary: Inflected Forms,” Merriam-Webster Online, 2015, accessed March 27, 2016, http://www.merriam-webster.com/help/explanatory-notes/dict-inflected-forms.