Set a Fixed div to 100% width of the parent container

You can use margin for .wrap container instead of padding for .wrapper:

body{ height:20000px }
#wrapper { padding: 0%; }
#wrap{ 
    float: left;
    position: relative;
    margin: 10%;
    width: 40%; 
    background:#ccc; 
}
#fixed{ 
    position:fixed;
    width:inherit;
    padding:0px; 
    height:10px;
    background-color:#333;    
}

jsfiddle