Javascript Category drop down help

Hey, this may not be the best place for this, but maybe someone can help me out quick. I am using the following for a drop down category menu in my archive page. All I want to do is make the width 100% in css. Is there a way to add a css class to this at all? Or, any way to change the width in pixes of the box? As it stands, it’s as wide as it needs to be. Thanks!

<script type="text/javascript"><!--
    var dropdown = document.getElementById("cat");
    function onCatChange() {
		if ( dropdown.options[dropdown.selectedIndex].value > 0 ) {
			location.href = "<?php echo get_option('home');
?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
		}
    }
    dropdown.onchange = onCatChange;
--></script>