Why Does Precision Loss Occur in JavaScript's number Type? How to Avoid Precision Loss Issues with number?

JavaScript's number type is based on the IEEE 754 standard for double-precision 64-bit floating-point representation. This representation leads to two primary precision issues:

1. Limited number of bits: In a 64-bit format, 1 bit is allocated for the sign, 11 bits for the exponent, and the remaining 52 bits for the significand (or fraction). This restricts the range and precision of numbers that can be represented exactly. When numbers exceed this exact range, rounding errors occur.

2. Limitations of binary floating-point: Not all decimal fractions can be represented exactly in binary. For example, the decimal value 0.1 is an infinite repeating fraction in binary, similar to how 1/3 cannot be represented exactly in decimal. In binary floating-point representation, such decimal numbers are approximated to finite binary representations, resulting in precision loss.

Example: When calculating 0.1 + 0.2 in JavaScript, the expected result is 0.3, but the actual result is often 0.30000000000000004, demonstrating the precision loss issue.

To avoid this precision loss, the following strategies can be used:

1. Integer arithmetic: Convert floating-point numbers to integers, perform the operation, and convert back. This approach is suitable for simple arithmetic operations like addition, subtraction, multiplication, and division.

   javascript
   // Example: Using integer arithmetic to avoid precision loss
   let result = (0.1 * 10 + 0.2 * 10) / 10; // Result is 0.3

2. Using third-party libraries: For more complex mathematical operations and to avoid precision loss, libraries such as BigNumber.js or decimal.js can be employed, which provide enhanced numerical precision.

   javascript
   // Example using BigNumber.js
   BigNumber.config({ DECIMAL_PLACES: 10 });
   let a = new BigNumber(0.1);
   let b = new BigNumber(0.2);
   let result = a.plus(b); // '0.3'

3. Built-in BigInt type: For integer operations, ES2020 introduced the BigInt type, which supports arbitrary-precision integers. Using BigInt avoids precision loss in large integer calculations, though it is not applicable to floating-point numbers.

   javascript
   // Example: Using BigInt for large integer calculations
   let bigInt1 = BigInt("9007199254740993");
   let bigInt2 = BigInt("1");
   let result = bigInt1 + bigInt2; // 9007199254740994n

In summary, to address precision issues with JavaScript's number type, developers should select appropriate methods based on the specific context to ensure numerical accuracy. For common decimal precision problems, converting to integer arithmetic is typically the simplest solution; for more complex scenarios, third-party libraries or the BigInt type may be necessary.