This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 7 years ago.
Today I have entered random float number and multipled by hundred firstly using normal code and then in console as was giving me wrong number, console is returning me the same.
The given float number is: 1050.6
Therefore: 1050.6 * 100 should be 105060, but javascript is returning me 105059.99999999999
Anyone knows why?
JavaScript uses 64-bit floating point representation (double precision). Numbers are represented in this format as a whole number multiplied by a power of two.
This is based on the IEEE 754 standard
Rational numbers with a denominator that isn't a power of 2 can't be exactly represented. This is why floating point multiplication gives this result.
Source: https://en.wikipedia.org/wiki/IEEE_floating_point
If you want to get the real value, there are two methods you can use
Rounding with Math.round
Math.round(1050.6 * 100)
Or toFixed
(1050.6 * 1000).toFixed(0)
It's a feature of how computers handle floating point numbers. It turns out that decimal numbers can't always be perfectly represented in binary so the computer gives the closest approximation it can.
https://en.wikipedia.org/wiki/IEEE_floating_point
Related
This question already has answers here:
What is JavaScript's highest integer value that a number can go to without losing precision?
(21 answers)
Closed 4 months ago.
How to increase this number(you can try it on the browser console):
36893488147419103000 + 1
The result of this is:
36893488147419103000
The number stays the same no changes to it why is that? and how can I increase it by 1?
For big integers you should use the BigInt (Big Integer) type.
Note 1: you almost always cannot mix BigInt numbers with Numbers (eg for math operations) without first performing an explicit conversion.
Note 2: JSON does not currently natively support BigInt values. As a workaround you can use strings (eg. '1n' for the values and then use a reviver function when calling JSON.parse.
JavaScript currently only has two numeric types: double-precision IEEE 754 floating point Numbers, and Big Integers which can be used to represent arbitrarily large integers. You can declare a BigInt number literal using the suffix n, eg. 1n.
IEEE 754 Numbers can "only" accurately represent integers up to and including Number.MAX_SAFE_INTEGER, which has a value of 2^53 - 1 or 9,007,199,254,740,991 or ~9 quadrillion.
From MDN:
Double precision floating point format only has 52 bits to represent the mantissa, so it can only safely represent integers between -(253 – 1) and 253 – 1. "Safe" in this context refers to the ability to represent integers exactly and to compare them correctly. For example, Number.MAX_SAFE_INTEGER + 1 === Number.MAX_SAFE_INTEGER + 2 will evaluate to true, which is mathematically incorrect. See Number.isSafeInteger() for more information.
A "Decimal" number type, that will be able to represent arbitrarily precise decimal numbers, is under development.
Obviously the number is internally represented as a floating point number.When the value you want do add to this number is less then the value of the least significant bit, it will not change the the value.
The only way would be to use floating point numbers with a higher resolution i.e. with a higher number of significant bits.
Double precision floating point format only has 52 bits to represent the mantissa, so it can only safely represent integers between -(253 – 1) and 253 – 1. See Number.MAX_SAFE_INTEGER. Larger numbers may not be able to be represented exactly.
This question already has answers here:
What is JavaScript's highest integer value that a number can go to without losing precision?
(21 answers)
Closed 8 years ago.
Can anybody solve the following problem with javascript
var i = 10152233307863175;
alert(i.toString());
alert shows value 10152233307863176. Any solution. Problem is when I get json object on client and when string is converted to json it contains wrong values.
This is a limitation in the precision of the numeric data format that javascript uses (double precision floating point).
The best way of storing that value, assuming you don't need to do any mathematical operations, is storing it as a string in the first place.
MDN has this to say about numbers in JavaScript.
Numbers in JavaScript are "double-precision 64-bit format IEEE 754 values", according to the spec.
There is no real integers in JavaScript. According to this source:
ECMAScript numbers are represented in binary as IEEE-754 (IEC 559) Doubles, with a resolution of 53 bits, giving an accuracy of 15-16 decimal digits; integers up to just over 9e15 are precise, ...
Your number 10152233307863175 contains 17 digits. Since the number is represented as a floating point number, JavaScript tries to do it's best and set bits in a way that the resulting number is closest to the supplied number.
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 9 years ago.
I tried this expression in both my FireFox and Chrome console:
17.99 * 100;
Expected Result: 1799
Actual Result: 1798.9999999999998
I also tried:
parseInt(17.99 * 100);
Expected Result: 1799
Actual Result: 1798
Why is this happening, and how do I get the expected result?
Floating point arithmetic isn't an exact science. The reason is that in memory, your precision is stored in binary (all powers of two). If it can't be represented by an exact power of two you can get some lost precision.
Your number, 1798.9999999999998 had enough lost precision that it didn't round up in the multiplication.
http://en.wikipedia.org/wiki/IEEE_floating_point
Try this:
Math.round(17.99*100)
As the previous answer explained, multiplying a float number is not exact science; what you can do is to expect a result in a certain precision range. Take a look at Number.prototype.toPrecision().
(17.99*100).toPrecision(4)
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 9 years ago.
I want to make multiplication using JavaScript.
Multiplication of 2 and 0.15 is 0.3 but 3 and 0.15 is 0.44999999999999996. I want to get 0.45 such as result. How can I do it with JavaScript?
It's a rounding error. You may want to round your number to a fixed amount of digits, like this:
parseFloat((your_number).toFixed(2));
Unfortunately this happens in any language using floating point arithmetic. It's an artifact arising when floating point operations are encoded into binary, operations performed, and decoded from binary to report the answer in a form you'd expect.
Depending on what you want to do with the output, you can call a round()-like function to round to a number of decimal places or compare the output to a value using a (small) number called a tolerance. E.g. two numbers are considered equal if their absolute difference is less than this tolerance.
This question already has answers here:
Why does floating-point arithmetic not give exact results when adding decimal fractions?
(31 answers)
Closed 9 years ago.
Why this will not give the results as expected?
console.log(0.2+0.1); // gives 0.30000000000000004
console.log(0.2+0.3); // gives 0.5
console.log(0.2+0.5); // gives 0.7
console.log(0.2+0.4); // gives 0.6000000000000001
Why the first and last will not give the results as expected?
It’s because JavaScript used the IEEE Standard for Binary Floating-Point Arithmetic.
All floating point math is like this and is based on the IEEE 754 standard. JavaScript uses 64-bit floating point representation, which is the same as Java's double.
Can be possible duplicate of Is floating point math broken?
Try .toFixed() .This method formats a number with a specific number of digits to the right of the decimal.
console.log((0.2 + 0.1).toFixed(1)); // gives 0.3
console.log((0.2 + 0.3).toFixed(1)); // gives 0.5
console.log((0.2 + 0.5).toFixed(1)); // gives 0.7
console.log((0.2 + 0.4).toFixed(1)); // gives 0.6