ToNumber applied to strings applies the following grammar to the input string. If the grammar cannot interpret the string as an expansion of StringNumericLiteral , then the result of ToNumber is NaN .

StringNumericLiteral :::

StrWhiteSpace_opt
StrWhiteSpace_opt StrNumericLiteral StrWhiteSpace_opt

StrWhiteSpace :::

StrWhiteSpaceChar StrWhiteSpace_opt

StrWhiteSpaceChar :::

<TAB>
<SP>
<FF>
<VT>
<CR>
<LF>

StrNumericLiteral :::

StrDecimalLiteral
+ StrDecimalLiteral
- StrDecimalLiteral
HexIntegerLiteral

StrDecimalLiteral :::

Infinity
DecimalDigits . DecimalDigits_opt ExponentPart_opt
. DecimalDigits ExponentPart_opt
DecimalDigits ExponentPart_opt

DecimalDigits :::

DecimalDigit
DecimalDigits DecimalDigit

DecimalDigit ::: one of

0 1 2 3 4 5 6 7 8 9

ExponentPart :::

ExponentIndicator SignedInteger

ExponentIndicator ::: one of

e E

SignedInteger :::

DecimalDigits
+ DecimalDigits
- DecimalDigits

HexIntegerLiteral :::

0x HexDigit
0X HexDigit
HexIntegerLiteral HexDigit

HexDigit ::: one of

0 1 2 3 4 5 6 7 8 9 a b c d e f A B C D E F

Some differences should be noted between the syntax of a StringNumericLiteral and a NumericLiteral (section 7.7.3):

• A StringNumericLiteral may be preceded and/or followed by whitespace and/or line terminators.
• A StringNumericLiteral may not use octal notation.
• A StringNumericLiteral that is decimal may have any number of leading 0 digits.
• A StringNumericLiteral that is decimal may be preceded by + or - to indicate its sign.
• A StringNumericLiteral that is empty or contains only whitespaceis converted to +0 .

The conversion of a string to a number value is similar overall to the determination of the number value for a numeric literal (section 7.7.3), but some of the details are different, so the process for converting a string numeric literal to a value of Number type is given here in full. This value is determined in two steps: first, a mathematical value (MV) is derived from the string numeric literal; second, this mathematical value is rounded, ideally using IEEE 754 round-to-nearest mode, to a representable value of the number type.

• The MV of StringNumericLiteral ::: (an empty character sequence) is 0.
• The MV of StringNumericLiteral ::: StrWhiteSpace is 0.
• The MV of StringNumericLiteral ::: StrWhiteSpaceopt StrNumericLiteral StrWhiteSpaceopt is the MV of StrNumericLiteral , no matter whether whitespace is present or not.
• The MV of StrNumericLiteral ::: StrDecimalLiteral is the MV of StrDecimalLiteral .
• The MV of StrNumericLiteral ::: + StrDecimalLiteral is the MV of StrDecimalLiteral .
• The MV of StrNumericLiteral ::: - StrDecimalLiteral is the negative of the MV of StrDecimalLiteral . (Note that if the MV of StrDecimalLiteral is 0, the negative of this MV is also 0. The rounding rule described below handles the conversion of this signless mathematical zero to a floating-point +0 or − 0 as appropriate.)
• The MV of StrNumericLiteral ::: HexIntegerLiteral is the MV of HexIntegerLiteral .
• The MV of StrDecimalLiteral ::: Infinity is 1010000 (a value so large that it will round to + ∞).
• The MV of StrDecimalLiteral ::: DecimalDigits . is the MV of DecimalDigits .
• The MV of StrDecimalLiteral ::: DecimalDigits . DecimalDigits is the MV of the first DecimalDigits plus (the MV of the second DecimalDigits times 10 ^{− n} ), where n is the number of characters in the second DecimalDigit s.
• The MV of StrDecimalLiteral ::: DecimalDigits . ExponentPart is the MV of DecimalDigits times 10 ^e , where e is the MV of ExponentPart .
• The MV of StrDecimalLiteral ::: DecimalDigits . DecimalDigits ExponentPart is (the MV of the first DecimalDigits plus (the MV of the second DecimalDigits times 10 ^{− n} )) times 10 ^e , where n is the number of characters in the second DecimalDigit s and e is the MV of ExponentPart .
• The MV of StrDecimalLiteral :::. DecimalDigits is the MV of DecimalDigits times 10 ^{− n} , where n is the number of characters in DecimalDigit s.
• The MV of StrDecimalLiteral :::. DecimalDigits ExponentPart is the MV of DecimalDigits times 10 ^e − ⁿ , where n is the number of characters in DecimalDigit s and e is the MV of ExponentPart .
• The MV of StrDecimalLiteral ::: DecimalDigits is the MV of DecimalDigits .
• The MV of StrDecimalLiteral ::: DecimalDigits ExponentPart is the MV of DecimalDigits times 10 ^e , where e is the MV of ExponentPart .
• The MV of DecimalDigits ::: DecimalDigit is the MV of DecimalDigit .
• The MV of DecimalDigits ::: DecimalDigits DecimalDigit is (the MV of DecimalDigits times 10) plus the MV of DecimalDigit .
• The MV of ExponentPart ::: ExponentIndicator SignedInteger is the MV of SignedInteger .
• The MV of SignedInteger ::: DecimalDigits is the MV of DecimalDigits .
• The MV of SignedInteger ::: + DecimalDigits is the MV of DecimalDigits .
• The MV of SignedInteger ::: - DecimalDigits is the negative of the MV of DecimalDigits .
• The MV of DecimalDigit ::: 0 or of HexDigit ::: 0 is 0.
• The MV of DecimalDigit ::: 1 or of HexDigit ::: 1 is 1.
• The MV of DecimalDigit ::: 2 or of HexDigit ::: 2 is 2.
• The MV of DecimalDigit ::: 3 or of HexDigit ::: 3 is 3.
• The MV of DecimalDigit ::: 4 or of HexDigit ::: 4 is 4.
• The MV of DecimalDigit ::: 5 or of HexDigit ::: 5 is 5.
• The MV of DecimalDigit ::: 6 or of HexDigit ::: 6 is 6.
• The MV of DecimalDigit ::: 7 or of HexDigit ::: 7 is 7.
• The MV of DecimalDigit ::: 8 or of HexDigit ::: 8 is 8.
• The MV of DecimalDigit ::: 9 or of HexDigit ::: 9 is 9.
• The MV of HexDigit ::: a or of HexDigit ::: A is 10.
• The MV of HexDigit ::: b or of HexDigit ::: B is 11.
• The MV of HexDigit ::: c or of HexDigit ::: C is 12.
• The MV of HexDigit ::: d or of HexDigit ::: D is 13.
• The MV of HexDigit ::: e or of HexDigit ::: E is 14.
• The MV of HexDigit ::: f or of HexDigit ::: F is 15.
• The MV of HexIntegerLiteral ::: 0x HexDigit is the MV of HexDigit .
• The MV of HexIntegerLiteral ::: 0X HexDigit is the MV of HexDigit .
• The MV of HexIntegerLiteral ::: HexIntegerLiteral HexDigit is (the MV of HexIntegerLiteral times 16) plus the MV of HexDigit .

Once the exact MV for a string numeric literal has been determined, it is then rounded to a value of the Number type. If the MV is 0, then the rounded value is +0 unless the first non-whitespace character in the string numeric literal is ' - ', in which case the rounded value is − 0 . Otherwise, the rounded value must be the number value for the MV (in the sense defined in section 8.4), unless the literal includes a StrDecimalLiteral and the literal has more than 20 significant digits, in which case the number value may be either the number value for the MV of a literal produced by replacing each significant digit after the 20th with a 0 digit or the number value for the MV of a literal produced by replacing each significant digit after the 20th with a 0 digit and then incrementing the literal at the 20th digit position. A digit is significant if it is not part of an ExponentPart and (either it is not 0 or (there is a nonzero digit to its left and there is a nonzero digit, not in the ExponentPart , to its right)).

The operator ToString converts a number m to string format as follows:

1. If m is NaN , return the string "NaN" .
2. If m is +0 or − 0 , return the string "0" .
3. If m is less than zero, return the string concatenation of the string "-" and ToString(− m ).
4. If m is infinity, return the string "Infinity" .
5. Otherwise, let n , k , and s be integers such that k >= 1, 10 ^k − ¹ <= s < 10 ^k , the number value for s ⋅10 ⁿ − ^k is m , and k is as small as possible. Note that k is the number of digits in the decimal representation of s , that s is not divisible by 10, and that the least significant digit of s is not necessarily uniquely determined by these criteria.
6. If k <= n <= 21, return the string consisting of the k digits of the decimal representation of s (in order, with no leading zeroes), followed by n − k occurences of the character ' 0 '.
7. If 0 < n <= 21, return the string consisting of the most significant n digits of the decimal representation of s , followed by a decimal point ' . ', followed by the remaining k − n digits of the decimal representation of s .
8. If −6 < n <= 0, return the string consisting of the character ' 0 ', followed by a decimal point ' . ', followed by − n occurences of the character ' 0 ', followed by the k digits of the decimal representation of s .
9. Otherwise, if k = 1, return the string consisting of the single digit of s , followed by lowercase character ' e ', followed by a plus sign ' + ' or minus sign '−' according to whether n −1 is positive or negative, followed by the decimal representation of the integer abs( n −1) (with no leading zeros).
10. Return the string consisting of the most significant digit of the decimal representation of s , followed by a decimal point ' . ', followed by the remaining k −1 digits of the decimal representation of s , followed by the lowercase character ' e ', followed by a plus sign ' + ' or minus sign '−' according to whether n −1 is positive or negative, followed by the decimal representation of the integer abs( n −1) (with no leading zeros).

Note that if x is any number value other than − 0 , then ToNumber(ToString( x )) is exactly the same number value as x .

As noted, the least significant digit of s is not always uniquely determined by the requirements listed in step 5. The following specification for step 5 was considered, but not adopted:

(This paragraph is not part of the ECMAScript specification.) Let n , k , and s be be integers such that k ≥ 1, 10 ^k − ¹ <= s < 10 ^k , the number value for s ⋅10 ⁿ − ^k is m , and k is as small as possible. If there are multiple possibilities for s , choose the value of s for which s ⋅10 ⁿ − ^k is closest in value to m . If there are two such possible values of s , choose the one that is even.

While such a strategy is recommended to implementors, the actual rule is somewhat more permissive. Implementors of ECMAScript may find useful the paper and code written by David M. Gay for binary-todecimal conversion of floating-point numbers [Gay 1990].