Name for "decimals" in other bases?

Question

In grade school, numbers that use a positional notation along with a decimal point (to delimit integer and fractional parts of a number are called "decimals". This "point" notation is easily generalized to any base, e.g., in base 2, we can write the number 101.11, and the point is then called a binary point. But what is the number itself called—a "binary"? (doesn't sound right, somehow, but it is analogous to the base 10 term "decimal"). Surely we can't continue to call it a "decimal" given that the base isn't 10; that definitely doesn't seem right.

Is there a base-independent term for a positional number containing a radix point?

Thank you

Answer 1

Recall that "decimal" is an abbreviation for the correct term, which is "decimal fraction." The base $2$ analogue is called a dyadic rational, but could be called a dyadic fraction. I have seen the name "ternary fraction" for the base $3$ analogue. We could (and someone undoubtedly does) also speak of octal fractions, or hexadecimal fractions.

Answer 2

I've always called it a "binary decimal" (etc. for other bases), as opposed to the regular "binary number." These are obvious contradictions of terms, but it's always been clear (or at least, it's always been clear with its context). One might also use "binary fraction," an allusion to the phrase "decimal fraction."

In another question, a poster claimed that the term 'binary decimal' is vastly outdated. He noted that binary numbers, which I suppose should just be called binaries (like decimals), are better known as binary numerals. If you pay a lot of attention, you'll notice that my use of binary decimal is a bit different than his.

Really, though, fraction is the best word. Recall that all digits after the decimal point are called the "fractional part" of the number, even if they don't terminate and are not periodic.

Answer 3

The term decimal can be used used to denote a number system or a notation. Since it is a notation commonly used in everyday language it has acquired a non-rigorous naming pattern i.e. we call something in a "Decimal Fraction" notation a decimal. Since other notations/bases are not commonly used, numbers represented using such notation may not have names or common names. In such cases, i think you have leave-way to name notations as you please, the idea here is to communicate an idea as clearly as possible.

Answer 4

I would call numbers that are not integers non-integers, or possibly non-integral or fractional numbers if I really wanted an adjective. This is a representation-independent concept — it just happens that it coincides with the set of numbers that cannot be written in positional notation, for any given base, without a radix point.

For the digits after the radix point themselves, that's exactly what I'd call them. It's a bit verbose, but gets the point across unambiguously. Should I find myself wanting a shorter name for them, I might try fractional digits (and substitute digits with the appropriate base-specific name, such as bits, if there is one) or perhaps $n$-ary places by analogy with "decimal places" (again substituting the appropriate name for $n$-ary).