DCMTK

dcm2json uses the method DcmJsonFormat::normalizeDecimalString() to normalize DICOM DS values before writing them as JSON.
However, the method currently does not catch all cases where a legal DICOM DS value is not permitted in JSON.
The JSON type number is defined in https://www.rfc-editor.org/rfc/rfc7159#section-6 as follows:

number = [ minus ] int [ frac ] [ exp ]
      decimal-point = %x2E       ; .
      digit1-9 = %x31-39         ; 1-9
      e = %x65 / %x45            ; e E
      exp = e [ minus / plus ] 1*DIGIT
      frac = decimal-point 1*DIGIT
      int = zero / ( digit1-9 *DIGIT )
      minus = %x2D               ; -
      plus = %x2B                ; +
      zero = %x30                ; 0

The definition of DICOM DS relies on the ANSI X3.9 standard, i.e. the specification of FORTRAN. The FORTRAN 'signed-real-literal-constant' is defined (in slightly simplified form) as:

R709 kind-param is digit-string or scalar-int-constant-name
R710 signed-digit-string is [ sign ] digit-string
R711 digit-string is digit [ digit ] ...
R712 sign is + or –
R713 signed-real-literal-constant is [ sign ] real-literal-constant
R714 real-literal-constant is significand [ exponent-letter exponent ] or digit-string exponent-letter exponent 
R715 significand is digit-string . [ digit-string ] or . digit-string
R716 exponent-letter is E or D
R717 exponent is signed-digit-string

As a regular expression, DICOM DS values can thus be defined as

[+-]?([0-9]+.[0-9]*|.?[0-9]+)(E[+-]?[0-9]+)?

Differences between JSON number and DICOM DS are thus:

1. JSON does not permit a leading '+' in the significand (i.e. "+1.0" is valid in DICOM but not in JSON)
2. JSON does not permit leading zeroes in the significand (i.e. "0003" is valid in DICOM but not in JSON)
3. JSON does not permit a leading '.' in the significand (i.e. ".5" is valid in DICOM but not in JSON)
4. JSON does not permit a trailing '.' in the significand (i.e. "5." is valid in DICOM but not in JSON)

DcmJsonFormat::normalizeDecimalString() currently accounts for differences 1 and 3, but not for 2 and 4. This should be fixed.