This is "By Design". The parseFloat function will only consider the parts of the string up until in reaches a non +, -, number, exponent or decimal point. Once it sees the comma it stops looking and only considers the "75" portion.

• https://developer.mozilla.org/en/JavaScript/Reference/Global_Objects/parseFloat

To fix this convert the commas to decimal points.

var fullcost = parseFloat($("#fullcost").text().replace(',', '.'));

Yes remove the commas:

let output = parseFloat("2,299.00".replace(/,/g, ''));
console.log(output);

You can use default parameters to automatically assign a value if none is given.

function neat(numToFormat, thousandSep = ".", decimalSep = ",")

You should start by checking if the input is valid, instead of doing it at the end. It would also be better to throw an error, since it's not easy to tell from the result if the formatting succeeded or not.

if (typeof numToFormat == 'number') {
  if(Number.isNaN(numToFormat) || !Number.isFinite(numToFormat)) {
    throw new Error("Invalid number");
  }
}
else if(typeof numToFormat == 'string') {
  if(!/^\d+((,|\.)\d+)?$/.test(numToFormat)) {
    throw new Error("Invalid string");
  }
}
else {
  throw new Error("Can only use number or string");
}

It's not parseFloat() which is imprecise, but the numbers themselves. JavaScript uses IEEE 754, which is 64-bit floating point numbers, with 53 bits used for precision. The number you are testing against is the highest safe integer, which is 2^53-1 and can be gotten from Number.MAX_SAFE_INTEGER. But your result could still be imprecise with numbers this large, since you are not only using integers but also 2 decimal places.

With string inputs you can get around this by not converting it to a number at all. Since the result is also a string, you can keep it a string all the way through. For number inputs you can only work with the precision you've been given. Any imprecision should be handled by the code calling this function beforehand.

You will need to update your parseInput function to avoid parseFloat. Just cut of any extra decimals, or add them if they are missing. If you want to round the number it gets a bit harder, but it's still possible.

Your placeThousands function can be done a little simpler. There are several ways to do it, but I would cut the string into an array of chunks and then join them together. I would also make it easier to change the chunk size by putting it in a variable.

const chunkSize = 3;
let chunks = [];
let start = wholesPart.length % chunkSize;
if(start != 0) {
    chunks.push(wholesPart.slice(0, start));
}
for(let i = start; i < wholesPart.length; i+= chunkSize) {
    chunks.push(wholesPart.slice(i, i + chunkSize));
}
return chunks.join(thousandSep)

When I saw fstChunk the first thing I thought was 'fast chunk', but I guess it's supposed to be 'first chunk'. There is no reason make things less clear just to save 2 characters.

You don't need to check the length of wholesPart, placeThousands can handle short strings.

return placeThousands(wholesPart) + decimalPart;

How can I tell jQuery/Javascript to interpret the . in 128.814 as a thousands separator and not a decimal point?

Simplest way would be to remove it.

When you remove it, it will automatically be interpreted as a thousands value, even without the comma there. Then, manually format the number like in How to print a number with commas as thousands separators in JavaScript

function addTotalPrice(item){
    var priceItem = parseFloat( $(item).find('.price').text().replace('.','') );
    var priceTotal = parseFloat( $('.label-price span').text().replace('.','') );

    var result = (priceTotal + priceItem);
    $('.label-price span').text( result.toString().replace(/\B(?=(\d{3})+(?!\d))/g, "."); );
}

var priceItem = parseFloat('900'.replace('.', ''));
var priceTotal = parseFloat('128.814'.replace('.', ''));

var result = (priceTotal + priceItem);
var fixedResult = result.toString().replace(/\B(?=(\d{3})+(?!\d))/g, ".");
document.write(fixedResult);

parseFloat( theString.replace(/,/g,'') );

According to the specification, a DecimalLiteral is defined as:

DecimalLiteral ::
    DecimalIntegerLiteral . DecimalDigitsopt ExponentPartopt 
    . DecimalDigits ExponentPartopt 
    DecimalIntegerLiteral ExponentPartopt

and for satisfying the parseFloat argument:

1. Let inputString be ToString(string).
2. Let trimmedString be a substring of inputString consisting of the leftmost character that is not a StrWhiteSpaceChar and all characters to the right of that character.(In other words, remove leading white space.)
3. If neither trimmedString nor any prefix of trimmedString satisfies the syntax of a StrDecimalLiteral (see 9.3.1), return NaN.
4. Let numberString be the longest prefix of trimmedString, which might be trimmedString itself, that satisfies the syntax of a StrDecimalLiteral.
5. Return the Number value for the MV

So numberString becomes the longest prefix of trimmedString that satisfies the syntax of a StrDecimalLiteral, meaning the first parseable literal string number it finds in the input. Only the . can be used to specify a floating-point number. If you're accepting inputs from different locales, use a string replace:

function parseLocalNum(num) {
    return +(num.replace(",", "."));
}

The function uses the unary operator instead of parseFloat because it seems to me that you want to be strict about the input. parseFloat("1ABC") would be 1, whereas using the unary operator +"1ABC" returns NaN. This makes it MUCH easier to validate the input. Using parseFloat is just guessing that the input is in the correct format.

The reference cited in the original answer below was wrong. There is a built in function for this, which is exactly what kaiser suggests below: toLocaleString

So you can do:

(1234567.89).toLocaleString('en')              // for numeric input
parseFloat("1234567.89").toLocaleString('en')  // for string input

The function implemented below works, too, but simply isn't necessary.

(I thought perhaps I'd get lucky and find out that it was necessary back in 2010, but no. According to this more reliable reference, toLocaleString has been part of the standard since ECMAScript 3rd Edition [1999], which I believe means it would have been supported as far back as IE 5.5.)

Original Answer

According to this reference there isn't a built in function for adding commas to a number. But that page includes an example of how to code it yourself:

function addCommas(nStr) {
    nStr += '';
    var x = nStr.split('.');
    var x1 = x[0];
    var x2 = x.length > 1 ? '.' + x[1] : '';
    var rgx = /(\d+)(\d{3})/;
    while (rgx.test(x1)) {
            x1 = x1.replace(rgx, '$1' + ',' + '$2');
    }
    return x1 + x2;
}

Edit: To go the other way (convert string with commas to number), you could do something like this:

parseFloat("1,234,567.89".replace(/,/g,''))

Do a replace first:

parseFloat(str.replace(',','.').replace(' ',''))

function seprator(input) {
  let nums = input.value.replace(/,/g, '');
  if (!nums || nums.endsWith('.')) return;
  input.value = parseFloat(nums).toLocaleString();
}

<input type="text" id="inputSep" oninput="seprator(this)" placeholder="123,456,789"/>

codepen example link