Convert the number into a string, match the number up to the second decimal place:

function calc(theform) {
    var num = theform.original.value, rounded = theform.rounded
    var with2Decimals = num.toString().match(/^-?\d+(?:\.\d{0,2})?/)[0]
    rounded.value = with2Decimals
}

<form onsubmit="return calc(this)">
Original number: <input name="original" type="text" onkeyup="calc(form)" onchange="calc(form)" />
<br />"Rounded" number: <input name="rounded" type="text" placeholder="readonly" readonly>
</form>

The toFixed method fails in some cases unlike toString, so be very careful with it.

You could use Math.floor and some additional arithmetics:

Math.floor(15.7784514000 * 100) / 100

Or convert the number into a string, match the number up to the second decimal place and turn it back into a number:

Number(15.7784514000.toString().match(/^\d+(?:\.\d{0,2})?/))

Then you can still call toFixed to get a string with a fixed number of decimal places.

var num1 = Math.floor(15.7784514000 * 100) / 100;
console.log(num1);

var num2 = Number(15.7784514000.toString().match(/^\d+(?:\.\d{0,2})?/));
console.log(num2)
console.log(num2.toFixed(2))

(Math.round(num * 100) / 100).toFixed(2);

Live Demo

var num1 = "1";
document.getElementById('num1').innerHTML = (Math.round(num1 * 100) / 100).toFixed(2);

var num2 = "1.341";
document.getElementById('num2').innerHTML = (Math.round(num2 * 100) / 100).toFixed(2);

var num3 = "1.345";
document.getElementById('num3').innerHTML = (Math.round(num3 * 100) / 100).toFixed(2);

span {
    border: 1px solid #000;
    margin: 5px;
    padding: 5px;
}

<span id="num1"></span>
<span id="num2"></span>
<span id="num3"></span>

Note that it will round to 2 decimal places, so the input 1.346 will return 1.35.