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I know that sometimes the notation .x is used as a short form of 0.x, but I've never heard about x. being a correct number (for instance, 3.). I want to know if it's technically correct to use a short-hand notation with leading/ending dot instead of the full notation. For instance, can numbers 3., .75 and 3.e10 be considered correct or not?

Ivan Yurchenko
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    Define official. – lhf Jul 18 '17 at 14:08
  • any notation is correct if it is understood correctly. But the notation $3.$ seems not useful out of language programming or something related to representation of float points. – Masacroso Jul 18 '17 at 14:10
  • If you write in Excel "3," (Excel uses "," instead of "." for the decimal separator) it write "3" on the screen, without complaints. – Mauro ALLEGRANZA Jul 18 '17 at 14:10
  • The '3.' notation is used in some programming languages for floats as a shorthand for 3.0 . One could also make a point for significant figures (if your number is only precise to the units digit) – Tob Ernack Jul 18 '17 at 14:10
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    There is no concept of being "approved for official use" with math notation. Sometimes something like 3. can be used in programming languages to force a value to be a float data type, or at least to emphasize that it is a float as opposed to an int data type. –  Jul 18 '17 at 14:12
  • It should be noted that the $0.3$ format is preferred over $.3$ in important contexts. For example, if you want to write a note saying some patient needs $.3\ \rm mg$ of a certain medication, you don't want to risk someone not noticing the decimal point and accidentally administering ten times the correct amount. (This is especially true for handwritten notes) – Akiva Weinberger Jul 18 '17 at 14:55
  • @MauroALLEGRANZA, doesn't the decimal separator depend on what locale you use? – md2perpe Jul 18 '17 at 15:33
  • And what happens if the number is to end a sentence? e.g., "The legislature considered the bill declaring $\pi = 3.$ But then it was time for the August recess." – Robert Soupe Jul 20 '17 at 05:22

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Often $.3$ will be used as shorthand for $0.3$. I emphasize shorthand cause you really should only ever do this in handwriting that only yourself will be reading. And even then, how much harder is it to write the extra $0$?

Something like $3.$ you might see often in programming languages. Computers treat and store floating point numbers differently than integers, so something like 3. or 3f is used to designate a floating point number. However, again, it is better to write $3.0$, because it is clearer what you mean and not that much harder to write.

Edit: In response to your comment asking if it is "technically correct" or "wrong", there are lots of notational differences among the mathematical community, however, there are only two real standards: correctness and clarity. And some of the best writing often emphasizes the latter over the former. In this case, I'd say it is certainly more clear to write $3.0$

Dando18
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Never mind "official use". Concentrate on clarity and write $0.3$ and $3.0$.

lhf
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