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.

To convert a string to a Number you can use the Number constructor:

const n = Number('my string') // NaN ("not a number")

To check to see if the conversion was a valid number:

Number.isNaN(n)

Note: Internet Explorer does not support Number.isNaN and for that you can use the older isNaN. More here and here.

To check if a Number is an integer, there are two built-in methods:

1. Number.isInteger(), and
2. Number.isSafeInteger()

Further discussion can be found here.

let a = [4, 2.3, "SO2", 4, "O2", 3.4, 4.5, "CO2", 5.6, 3.4, 2];

a.forEach((e)=>{
    const n = Number(e)

    if (Number.isNaN(n)) {
        console.log(e + " :letter")
        return
    }

    if (Number.isInteger(n)) {
        console.log(e + " :integer")
        return
    }

    console.log(e + " :non-integer number")
})

Note

“Floating point” is the name of the technology used to represent the numbers in binary. This is why I changed the terminology from "float" to "non-integer number" in the code above.

Some numeric values in JavaScript contain non-numeric characters. eg.

Infinity
0x3d // hexadecimal
3n // BigInt
0b101011 // Binary
1e2 // times ten to the power of...

There are now two kinds of number in JavaScript: Number and BigInt.

Number is an implementation of the IEEE 754 32-bit floating point number specification.

var intvalue = Math.floor( floatvalue );
var intvalue = Math.ceil( floatvalue ); 
var intvalue = Math.round( floatvalue );

// `Math.trunc` was added in ECMAScript 6
var intvalue = Math.trunc( floatvalue );

Math object reference

Examples

// value=x        //  x=5          5<x<5.5      5.5<=x<6  

Math.floor(value) //  5            5            5
Math.ceil(value)  //  5            6            6
Math.round(value) //  5            5            6
Math.trunc(value) //  5            5            5
parseInt(value)   //  5            5            5
~~value           //  5            5            5
value | 0         //  5            5            5
value >> 0        //  5            5            5
value >>> 0       //  5            5            5
value - value % 1 //  5            5            5

// value=x        // x=-5         -5>x>=-5.5   -5.5>x>-6

Math.floor(value) // -5           -6           -6
Math.ceil(value)  // -5           -5           -5
Math.round(value) // -5           -5           -6
Math.trunc(value) // -5           -5           -5
parseInt(value)   // -5           -5           -5
value | 0         // -5           -5           -5
~~value           // -5           -5           -5
value >> 0        // -5           -5           -5
value >>> 0       // 4294967291   4294967291   4294967291
value - value % 1 // -5           -5           -5

// x = Number.MAX_SAFE_INTEGER/10 // =900719925474099.1

// value=x            x=900719925474099    x=900719925474099.4  x=900719925474099.5
           
Math.floor(value) //  900719925474099      900719925474099      900719925474099
Math.ceil(value)  //  900719925474099      900719925474100      900719925474100
Math.round(value) //  900719925474099      900719925474099      900719925474100
Math.trunc(value) //  900719925474099      900719925474099      900719925474099
parseInt(value)   //  900719925474099      900719925474099      900719925474099
value | 0         //  858993459            858993459            858993459
~~value           //  858993459            858993459            858993459
value >> 0        //  858993459            858993459            858993459
value >>> 0       //  858993459            858993459            858993459
value - value % 1 //  900719925474099      900719925474099      900719925474099

// x = Number.MAX_SAFE_INTEGER/10 * -1 // -900719925474099.1

// value = x      // x=-900719925474099   x=-900719925474099.5 x=-900719925474099.6

Math.floor(value) // -900719925474099     -900719925474100     -900719925474100
Math.ceil(value)  // -900719925474099     -900719925474099     -900719925474099
Math.round(value) // -900719925474099     -900719925474099     -900719925474100
Math.trunc(value) // -900719925474099     -900719925474099     -900719925474099
parseInt(value)   // -900719925474099     -900719925474099     -900719925474099
value | 0         // -858993459           -858993459           -858993459
~~value           // -858993459           -858993459           -858993459
value >> 0        // -858993459           -858993459           -858993459
value >>> 0       //  3435973837           3435973837           3435973837
value - value % 1 // -900719925474099     -900719925474099     -900719925474099

There are functions to round numbers. For example:

var x = 5.0364342423;
print(x.toFixed(2));

will print 5.04.

EDIT: Fiddle

From the Floating-Point Guide:

What can I do to avoid this problem?

That depends on what kind of calculations you’re doing.

• If you really need your results to add up exactly, especially when you work with money: use a special decimal datatype.
• If you just don’t want to see all those extra decimal places: simply format your result rounded to a fixed number of decimal places when displaying it.
• If you have no decimal datatype available, an alternative is to work with integers, e.g. do money calculations entirely in cents. But this is more work and has some drawbacks.

Note that the first point only applies if you really need specific precise decimal behaviour. Most people don't need that, they're just irritated that their programs don't work correctly with numbers like 1/10 without realizing that they wouldn't even blink at the same error if it occurred with 1/3.

If the first point really applies to you, use BigDecimal for JavaScript or DecimalJS, which actually solves the problem rather than providing an imperfect workaround.