I want to know if numbers should be written alphabetically in educational contexts, for instance:
10 plasma samples out of 1016 cannot be ignored.
Ten plasma samples out of one thousand and sixteen cannot be ignored.
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For a technical journal, you would want to use numerals, not spell out the numbers.
Our journals follow The Associated Press Stylebook style (for the most part), which means that we do spell out numbers less than 10, but use numerals for numbers 10 and greater. We also use numerals when the numeral is followed by a unit of measurement, even if the numeral is less than 10. And we would not use a numeral to begin a sentence. (So in your example, we would use this: "Ten plasma samples out of 116 cannot be ignored." Or "Ten plasma samples out of 1016 cannot be ignored." (If you actually meant to write out one-thousand and sixteen.)
Also, if your paper is accepted, most journals will have editors helping you with the style in your back-and-forth communications.
There is no single standard, but some things to consider:
Also, please note that the expanded word form of 116 should be "one hundred sixteen", and that there is an inconsistency in your original post: is the value 116 or 1016?
Just a late thought: It depends on the impact you would like the number to have, if you use digits the visual reception of the quantity is immediate. The spelled-out words has lesser influence and to some extend obfuscates the number.
So I would think if the number is important it should be shown as digits, and if the application of the number is of greater concern it should be spelled-out.