Number

Standard 64-bit IEEE 754 floating-point numbers.

A number is a 64-bit double-precision floating-point value conforming to IEEE 754. Numbers are scalar values used to express integers, fractional values, and special numeric constants.

Numbers support several representations: decimal, the alternative bases (binary, octal, hexadecimal), scientific notation, and the special values NaN and Inf.

Syntax

A number can be written in several forms:

number = ["-" | "+"] (
    decimalNumber
  | binaryNumber
  | octalNumber
  | hexNumber
  | scientificNumber
) | specialValue

decimalNumber    = digit+ [ "." digit* ] | "." digit+
binaryNumber     = "0b" binaryDigit+
octalNumber      = "0o" octalDigit+
hexNumber        = "0x" hexDigit+
scientificNumber = ( digit+ [ "." digit* ] | "." digit+ ) ("e" | "E") ["-" | "+"] digit+
specialValue     = "NaN" | "Inf" | "-Inf" | "+Inf"

digit       = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
binaryDigit = "0" | "1"
octalDigit  = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7"
hexDigit    = digit | "A" | "B" | "C" | "D" | "E" | "F" | "a" | "b" | "c" | "d" | "e" | "f"

Structural characters

Symbol	Name	Unicode	Description
0–9	Digits	Multiple	Decimal digits
.	Decimal point	U+002E	Separates the integer and fractional parts
-	Minus sign	U+002D	Negative value
+	Plus sign	U+002B	Explicit positive value (not preserved on output)
e / E	Exponent	Multiple	Scientific-notation exponent
0b	Binary prefix	Multiple	Begins a binary number
0o	Octal prefix	Multiple	Begins an octal number
0x	Hex prefix	Multiple	Begins a hexadecimal number

Valid forms

Decimal numbers

Decimal numbers may be integers or fractional values, with an optional sign. A leading or trailing decimal point is allowed (.5 and 5.).

# Integers
42                   # integer
-17                  # negative integer
+17                  # positive integer (explicit sign, not preserved)

# Fractional
3.14159              # fractional
-0.5                 # negative fractional
.5                   # leading dot -> 0.5
5.                   # trailing dot -> 5

# Zero
0
+0
-0

Alternative bases

Numbers can be written in binary, octal, or hexadecimal. The prefix is case-insensitive, and hex digits may be upper or lower case.

# Binary (0b / 0B), digits 0-1
0b1010               # 10
0B1111               # 15
-0b1010              # -10

# Octal (0o / 0O), digits 0-7
0o755                # 493
0O644                # 420

# Hexadecimal (0x / 0X), digits 0-9 A-F
0xFF                 # 255
0XDeadBeef           # 3735928559
0xff                 # 255 (lower-case digits)

Scientific notation

Scientific notation uses e or E (case-insensitive) for the exponent, which may be signed.

1.23e4               # 1.23 × 10^4  = 12300
1.23e-4              # 1.23 × 10^-4 = 0.000123
-2.5e+3              # -2.5 × 10^3  = -2500
5e3                  # 5 × 10^3     = 5000
.5e2                 # 0.5 × 10^2   = 50
6.022e23             # Avogadro's number

Equivalent forms

The same value can be written in several bases and notations:

---
42, 0x2A, 0b101010, 0o52, 4.2e1

All five values above are 42.

Invalid forms

The following are genuine syntax errors (the parser reports an error):

---
0o89                 # ✗ invalid octal digit

0b                   # ✗ missing binary digits
0x                   # ✗ missing hex digits
0xGH                 # ✗ invalid hex digits
0b 1010              # ✗ space between the prefix and the digits

Implementation status (beta)

The reference implementation is currently lenient with some malformed numeric tokens. These are tracked as implementation issues; a conformant parser SHOULD reject them rather than accept or coerce them:

• An incomplete exponent is accepted instead of rejected: 1e and 1e+ both yield 1.

• A token that begins like a number but is ill-formed falls back to an open string instead of raising an error: 0b12 → "0b12", 1.2.3 → "1.2.3", 1.23ee4 → "1.23ee4".

Preservation of structure

Internet Object preserves:

• The chosen notation (decimal, binary, octal, hex, scientific)

• Whitespace (non-significant)

• Syntactic fidelity as written, except that an explicit + sign is not preserved

It does not interpret:

• Mathematical relationships between values

• Precision beyond IEEE 754

• Domain-specific numeric constraints

Those semantics belong to the schema, the validator, or the application.

See Also

• Numeric Values — all numeric forms and notations

• BigInt — arbitrary-precision integers

• Decimal — fixed-precision decimal arithmetic

• NaN and Infinity — special numeric values

• Numeric Types — numeric schemas