How can I refer to a number written out in its decimal expansion (e.g., 1.25) or binary expansion (e.g., 1.01) to distinguish it from a number expressed as a fraction? I am teaching students to use different bases so do not want a term referencing a specific base, such as "decimal expansion".

In computer architecture, the term "floating point" (or "fixed point", depending on the implementation) is used, but I don't think this is a mathematical term.

In case, my question is unclear, I want to complete this analogy: $\frac{1}{2}$ is to fraction as .5 is to ?

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    $\begingroup$ Maybe 'digits expansion' could work. I think it is used occasionaly, but I doubt it is a common term. $\endgroup$ – quid Aug 2 '17 at 22:34
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    $\begingroup$ I think this is called "positional notation" with a radix point. $\endgroup$ – user52817 Aug 3 '17 at 3:04
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    $\begingroup$ I would just call it "floating point number". Terminology diffuses between mathematics and computer science. It is a natural term to use and just takes a few seconds to explain. $\endgroup$ – John Coleman Aug 3 '17 at 15:44
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    $\begingroup$ @JohnColeman: But the point doesn't float. $\endgroup$ – Daniel R. Collins Aug 3 '17 at 21:27
  • $\begingroup$ @DanielR.Collins Depends on how you think about it. I remember being taught to multiply and divide by powers of 10 by shifting the decimal point. When I learned how to program much later in life, I thought of that the first time that I encountered the term "floating point" and it struck me as being incredibly natural. $\endgroup$ – John Coleman Aug 3 '17 at 22:30

The point is definitely called, in general, the radix point (as stated in a comment by @user52817).

I'm not familiar with, nor succeeding at a search for, a general name for the representation method. I would be comfortable calling one an "$n$-ary representation", following the term decimal representation (similar to a comment by @mweiss).

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    $\begingroup$ Linguistically, then, based on the adjectival form of radix, you would think the term would be radical or radical representation, but sadly, those terms are already used for a different concept. $\endgroup$ – shoover Aug 3 '17 at 16:34
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    $\begingroup$ It is odd, though, that language seems to have settled on "$n$-ary" rather than "$n$-imal". I guess the latter sounds too much like "animal"? $\endgroup$ – mweiss Aug 3 '17 at 21:20
  • $\begingroup$ @mweiss Presumably "n-ary" is thought of as a generalization of "binary" and "trinary". $\endgroup$ – Jim Belk Aug 5 '17 at 17:46
  • $\begingroup$ Yes, obviously (although "ternary" is more common than "trinary") - but why those rather than a generalization of "decimal", "hexadecimal" and "sexagesimal"? $\endgroup$ – mweiss Aug 6 '17 at 2:00

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