Word for a number without formatting

An interesting question where the answer depends much more on defined convention than on dictionary usage. Your "plain" number and your "formatted" number are both "decimal" numbers.

Your "formatted" number is better termed a "grouped" decimal because of the international standards that apply:

A comma or a dot on a line are reaffirmed as decimal marker symbols, and not as grouping symbols in order to facilitate reading;

"numbers may be divided in groups of three in order to facilitate reading;

neither dots nor commas are ever inserted in the spaces between groups".

General Conference on Weights and Measures

Previous usage had groupings such as 123,234,432.993 but the use of commas and stops was potentially confusing and it makes sense to do away with all except the decimal separator (either the stop or the comma). You may see the confusion in examples like your own, or in this:

GB-English 4,294,967,295.000

Italian 4.294.967.295,000

https://docs.oracle.com/cd/E19455-01/806-0169/overview-9/index.html

The general conference specified the comma and the dot as decimal separators. It also specified that grouping should be done with spaces. Hence:

1234567.89 (or 1234567,89) are decimals

and 1 234 567.89 (or 1 234 567,89) may be termed "grouped decimals".

The written form of the numbers are all represented by the same to the computer. All three of the forms (1,234.56 / 1.234,56 / 1234.56) could be considered 'formatted'. That is because they are all representations of floating-point numbers.

It's not a single word, but floating-point representation would work for numeric, can-be-used-in-calculations representation.

A floating-point representation is the reason that a normal-looking number like 10.1 sometimes will get printed as 10.09999998. (The fractional 0.1 is a represented by a repeated binary mantissa.)