2nd/10_Wiki/Topic_JavaScript/JavaScript_Numbers.md

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id	title	category	status	verification_status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	created_at	updated_at	review_reason	merge_history	tags	raw_sources	applied_in	github_commit
javascript-numbers	JavaScript Numbers	Frontend	draft	conceptual		numbers JS numbers floating point NaN Infinity IEEE 754		B	0.89	2026-06-23	2026-06-23			javascript js web frontend w3schools numbers floating-point nan	https://www.w3schools.com/js/js_numbers.asp

JavaScript Numbers

🎯 한 줄 통찰 (One-line insight)

JavaScript has only one number type — a 64-bit IEEE 754 double — so integers are precise only to 15 digits, floating-point arithmetic can be imprecise, and special values NaN and Infinity are themselves of type number. [S1]

🧠 핵심 개념 (Core concepts)

• One number type — JavaScript has only one type of number; numbers can be written with or without decimals, and scientific notation (123e5) is allowed. [S1]
• Always 64-bit floating point — JavaScript numbers are always stored as double precision floating point following the IEEE 754 standard (fraction in bits 0-51, exponent in 52-62, sign in bit 63). [S1]
• Integer precision — integers are accurate up to 15 digits; the maximum number of decimals is 17. [S1]
• Floating precision — floating point arithmetic is not always 100% accurate (e.g. 0.2 + 0.1). [S1]
• + is addition AND concatenation — numbers are added; strings are concatenated; mixing them concatenates left-to-right. [S1]
• NaN — a reserved word meaning "not a legal number"; typeof NaN returns number; use isNaN() to test. [S1]
• Infinity — returned when a value exceeds the largest possible number, or on division by 0; typeof Infinity returns number. [S1]
• Hexadecimal — constants prefixed with 0x are interpreted as hexadecimal; toString() can output base 2 to base 36. [S1]
• Numbers as objects — new Number() creates an object; the page warns not to create Number objects. [S1]

🧩 추출된 패턴 (Extracted patterns)

• Fix floating drift — multiply and divide ((0.2 * 10 + 0.1 * 10) / 10) to work around floating-point imprecision. [S1]
• Guard against NaN — test inputs with isNaN() before using them in arithmetic, since NaN propagates through operations. [S1]
• Force numeric addition — beware that "10" + 20 concatenates; ensure operands are numbers when you intend addition. [S1]
• Base conversion — use number.toString(radix) to render in binary, octal, hex, or any base 2-36. [S1]

📖 세부 내용 (Details)

Number Types JavaScript has only one type of number. Numbers can be written with or without decimals. [S1]

let x = 3.14;    // A number with decimals
let y = 3;       // A number without decimals

Extra large or extra small numbers can be written with scientific (exponent) notation: [S1]

let x = 123e5;    // 12300000
let y = 123e-5;   // 0.00123

JavaScript Numbers are Always 64-bit Floating Point Unlike many other languages, JavaScript does not define different number types (integers, short, long, float, etc.). Numbers are always stored as double precision floating point following IEEE 754, in 64 bits: the fraction in bits 0-51, the exponent in bits 52-62, and the sign in bit 63. [S1]

Value (aka Fraction/Mantissa)	Exponent	Sign
52 bits (0 - 51)	11 bits (52 - 62)	1 bit (63)

JavaScript numbers are always double (64-bit floating point). [S1]

Integer Precision Integers (numbers without a period or exponent notation) are accurate up to 15 digits. The maximum number of decimals is 17. [S1]

let x = 999999999999999;   // x will be 999999999999999
let y = 9999999999999999;  // y will be 10000000000000000

Floating Precision Floating point arithmetic is not always 100% accurate: [S1]

let x = 0.2 + 0.1;

To solve the problem above, it helps to multiply and divide: [S1]

let x = (0.2 * 10 + 0.1 * 10) / 10;

Adding Numbers and Strings

Warning: JavaScript uses the + operator for both addition and concatenation. Numbers are added. Strings are concatenated. [S1]

Adding two numbers gives a number: [S1]

let x = 10;
let y = 20;
let z = x + y;

Adding two strings gives a concatenation: [S1]

let x = "10";
let y = "20";
let z = x + y;

Adding a number and a string gives a concatenation: [S1]

let x = 10;
let y = "20";
let z = x + y;

Adding a string and a number gives a concatenation: [S1]

let x = "10";
let y = 20;
let z = x + y;

A common mistake is to expect this to be 30: [S1]

let x = 10;
let y = 20;
let z = "The result is: " + x + y;

A common mistake is to expect this to be 102030: [S1]

let x = 10;
let y = 20;
let z = "30";
let result = x + y + z;

The JavaScript interpreter works from left to right. First 10 + 20 is added because x and y are both numbers; then 30 + "30" is concatenated because z is a string. [S1]

Numeric Strings JavaScript will try to convert strings to numbers in numeric operations. Division, multiplication, and subtraction work; addition concatenates. [S1]

let x = "100";
let y = "10";
let z = x / y;

let x = "100";
let y = "10";
let z = x * y;

let x = "100";
let y = "10";
let z = x - y;

This will NOT work (it concatenates): [S1]

let x = "100";
let y = "10";
let z = x + y;

NaN - Not a Number NaN is a JavaScript reserved word indicating that a number is not a legal number. Arithmetic with a non-numeric string yields NaN: [S1]

let x = 100 / "Apple";

If the string is numeric, the result is a number: [S1]

let x = 100 / "10";

Use isNaN() to test: [S1]

let x = 100 / "Apple";
isNaN(x);

NaN propagates through math: [S1]

let x = NaN;
let y = 5;
let z = x + y;

Or it concatenates like NaN5: [S1]

let x = NaN;
let y = "5";
let z = x + y;

typeof NaN returns number: [S1]

typeof NaN;

Infinity Infinity (or -Infinity) is returned for a number outside the largest possible number. [S1]

let myNumber = 2;
// Execute until Infinity
while (myNumber != Infinity) {
  myNumber = myNumber * myNumber;
}

Division by 0 also generates Infinity: [S1]

let x =  2 / 0;
let y = -2 / 0;

typeof Infinity returns number: [S1]

typeof Infinity;

Hexadecimal JavaScript interprets numeric constants as hexadecimal if they are preceded by 0x. [S1]

let x = 0xFF;

Never write a number with a leading zero (like 07); some versions interpret it as octal. By default JavaScript displays numbers as base 10, but toString() can output base 2 to base 36 (hex = base 16, decimal = base 10, octal = base 8, binary = base 2): [S1]

let myNumber = 32;
myNumber.toString(32);
myNumber.toString(16);
myNumber.toString(12);
myNumber.toString(10);
myNumber.toString(8);
myNumber.toString(2);

JavaScript Numbers as Objects Numbers are normally primitive values from literals, but can be defined as objects with new: [S1]

let x = 123;
let y = new Number(123);

Warning: Do not create Number objects. The new keyword complicates the code and slows down execution speed. [S1]

With ==, a primitive and a Number object are equal; with === they are not equal; and comparing two Number objects always returns false: [S1]

let x = 500;
let y = new Number(500);

let x = new Number(500);
let y = new Number(500);

🛠️ 적용 사례 (Applied in summary)

The page's own snippets are the canonical applied examples — demonstrating integer precision limits, the 0.2 + 0.1 floating drift fix, + concatenation pitfalls, isNaN() checks, the Infinity loop, and toString(radix) base conversions. No external project/commit applications found in the source.

💻 코드 패턴 (Code patterns)

Work around floating drift:

let x = (0.2 * 10 + 0.1 * 10) / 10;

Detect a non-number:

isNaN(100 / "Apple");

Convert to another base:

(32).toString(2);   // binary
(32).toString(16);  // hexadecimal

⚖️ 모순 및 업데이트 (Contradictions & updates)

Note that 0.2 + 0.1 does not produce exactly 0.3 due to IEEE 754 floating point; the page presents the multiply/divide workaround. No contradictions found in the source.

✅ 검증 상태 및 신뢰도

• 상태: draft
• 검증 단계: conceptual (실제 적용 사례 발견 시 applied/validated로 승격 가능)
• 출처 신뢰도: B (W3Schools — widely used educational reference, not a primary standards body)
• 신뢰 점수: 0.89
• 중복 검사 결과: 신규 생성 (New discovery)

🔗 지식 그래프 (Knowledge Graph)

• 상위/루트: JavaScript Tutorial
• 관련 개념: JavaScript Number Methods, JavaScript Data Types, JavaScript Operators, JavaScript BigInt
• 참조 맥락: The foundation for all numeric computation and the precision pitfalls behind money/financial calculations.

📚 출처 (Sources)

• [S1] W3Schools — JavaScript Numbers — https://www.w3schools.com/js/js_numbers.asp

📝 변경 이력 (Change history)

• 2026-06-23: Initial draft synthesized from the W3Schools "JavaScript Numbers" page (Astra wiki-curation, P-Reinforce v3.1 format).