What 17 decimal places of precision means in number js mdn doc?

Question

const a = 10;
const b = 0.123456789123456789;

console.log((a + b).toFixed(17));


// 10.12345678912345726

As you can see from example above, .12345678912345 , only this part are shown correctly , as I understand Javascript only consider 15 places precision ( including .). If I will change 10 to 100 , it will be same amount , but I was thinking it should be 17 places precision by MDN doc. What doesn't this phrase exactly mean 17 decimal places of precision ?

If I will show it without .toFixed() method , it will show same 15 precision 10.123456789123457 - response of a + b

Url: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number

Answer 1

According to JS/ECMAScript specification, the Number type uses double-precision floating point which has 64-bit format (binary64), consists of a sign bit (determines positive or negative value), 11 exponent bits and 52 fraction bits (each digit represents 4-bits, hence 64-bit has 16 digits):

The Number type representing the double-precision 64-bit format IEEE 754-2008 values as specified in the IEEE Standard for Binary Floating-Point Arithmetic.

The maximum positive number which can be represented properly using double precision is 9007199254740992, which can be achieved by using Math.pow(2, 53). If the number range is between Math.pow(2, 53) and Math.pow(2, 54) (or between Math.pow(2, -53) and Math.pow(2, -54)), only even numbers can be represented properly because the exponent bits will affect LSB (least-significant bit) on the fraction bits.

Let's review the large number part:

var x = 12345678912345.6789

var x = new Number(12345678912345.6789)

This number contains more than 52 fractional bits (72 bits in total), hence the rounding used to keep the fractional bits to 52.

Also with this decimal number:

var x = new Number(.12345678912367890)

This number contains 68 fractional bits, hence the last zero is chopped off to keep 64-bit length.

Usually numeric representation larger than 9007199254740992 or smaller than 1.1102230246251565E-16 are stored as literal strings instead of Number. If you need to compute very large numbers, there are certain external libraries available to perform arbitrary precision arithmetic.

If you want to cast more then 16 points after the decimal point you can either:

• Use literal string to represent your number
• Use external libraries like math.js, BigInteger.js or strint library.