How do I check that a number is float or integer?

check for a remainder when dividing by 1:

function isInt(n) {
   return n % 1 === 0;
}

If you don't know that the argument is a number you need two tests:

function isInt(n){
    return Number(n) === n && n % 1 === 0;
}

function isFloat(n){
    return Number(n) === n && n % 1 !== 0;
}

Update 2019 5 years after this answer was written, a solution was standardized in ECMA Script 2015. That solution is covered in this answer.

Try these functions to test whether a value is a number primitive value that has no fractional part and is within the size limits of what can be represented as an exact integer.

function isFloat(n) {
    return n === +n && n !== (n|0);
}

function isInteger(n) {
    return n === +n && n === (n|0);
}