|52 bits (0 – 51)||11 bits (52 – 62)||1 bit (63)|
If a number is too big, it would overflow the 64-bit storage, potentially giving an infinity:
console.log( 1e309 ); // Infinity console.log( 1e308 ); // 1e+308
Precision (or imprecision?!)
Integers are accurate up to 15 digits and by integers I mean numbers without a period or exponent notation.
var x = 999999999999999; // x will be 999999999999999 var y = 9999999999999999; // y will be 10000000000000000
The maximum number of decimals is 17, but floating point arithmetic is not always 100% accurate:
var x = 0.2 + 0.1; // x will be 0.30000000000000004
So, this will result in a false!
console.log( 0.1 + 0.2 == 0.3 ); // false
A number is stored in memory in its binary form, a sequence of bits – ones and zeroes. But fractions like 0.1, 0.2 that look simple in the decimal numeric system are actually unending fractions in their binary form.
In other words, what is 0.1? It is one divided by ten 1/10, one-tenth. In decimal numeral system such numbers are easily representable. Compare it to one-third: 1/3. It becomes an endless fraction 0.33333(3).
So, division by powers 10 is guaranteed to work well in the decimal system, but division by 3 is not. For the same reason, in the binary numeral system, the division by powers of 2 is guaranteed to work, but 1/10 becomes an endless binary fraction.
There’s just no way to store exactly 0.1 or exactly 0.2 using the binary system, just like there is no way to store one-third as a decimal fraction.
The numeric format IEEE-754 solves this by rounding to the nearest possible number. These rounding rules normally don’t allow us to see that “tiny precision loss”, but it exists.
The same issue exists in many other programming languages.
PHP, Java, C, Perl, Ruby give exactly the same result, because they are based on the same numeric format.
Work around the problem?
The most reliable method is to round the result with the help of a method
console.log( 0.1 + 0.2 == 0.3 ); // false let sum = 0.1 + 0.2; console.log( sum.toFixed(2) == 0.3 ); // true
toFixed always returns a string. It ensures that it has 2 digits after the decimal point. We can use the unary plus to coerce it into a number:
let sum = 0.1 + 0.2; console.log( +sum.toFixed(2) ); // 0.3
One more solution
var x = (0.2 * 10 + 0.1 * 10) / 10; // x will be 0.3
error numbers precision solution