Is it possible to use position: fixed with width: 100%?

Question

css

Good afternoon!
I have another stupid question (:
It is necessary to fix the top navigation. There is the following code:

<div class="wrapper">

  <div class="nav">
    <ul class="menu">
      <li><a href="">Menu</a>
        <ul>
          <li><a href="index.html" class="current">Home</a></li>
          <li><a href="#service">Service</a></li>
          <li><a href="#portfolio">Portfolio</a></li>
          <li><a href="#team">Team</a></li>
          <li><a href="#tarifs">Tarifs</a></li>
          <li><a href="#contact">Contact</a></li>
        </ul>
      </li>
    <ul>
  </div>
</div>

And styles for it:

@import url("reset.css");

html,
body{
  height: 100%;
}

.wrapper{
  position: relative;
  min-height: 100%;
  width: 100%;
  max-width: 320px;
  margin: 0 auto;
  font-size: 100%;
  font-family: "Open Sans", sans-serif;
}

.nav{

  position: fixed;
  top: 0;
  width: 100%;
  z-index: 9999;
  background: #000 url("../images/logo.png") no-repeat  1.5em 1em;
  line-height: 4em;
}
.nav ul li{
  width: 100%;
}
.nav li ul{
  display: none;
}
.nav .menu>li>a{
  color: #49cbcd;
  padding: 0.4em 1.563em;
  font-size: 1.2em;
  font-weight: bold;
  text-align:center;
  text-decoration: none;
}
.nav li ul li a{
  display: block;
  text-decoration: none;
  color: #484c55;
  text-align: center;
}
.nav li ul li a:hover{
  color: #90dbdd;
  border-bottom: 3px solid #49cbcd;
  background: #f8f9fb;
}
.nav li:hover ul{ 
  display: block;
}

In this form, the following happens:

Answer 1

Maybe.

Answer 2

Set left: 0;
jsfiddle.net/ag7qwcqz