ngmodel not binding integer values on select tag

I will be getting the selected value as integer from service and need to send it back as integer. please check the Plnkr for code

<!-- Working -->
<div ng-init="selectedvalue = '3'">
    <select ng-model="selectedvalue">
    <option value="1">1</option>
    <option value="2">2</option>
    <option value="3">3</option>
    <option value="4">4</option>
  </select>
</div>
<!-- Not Working -->
<div ng-init="selectedvalue2 = 3">
    <select ng-model="selectedvalue2">
    <option value="1">1</option>
    <option value="2">2</option>
    <option value="3">3</option>
    <option value="4">4</option>
  </select>
</div>
<!-- Not Working -->
<div ng-init="selectedvalue3 = 3">
    <select ng-model="selectedvalue3">
    <option value=1>1</option>
    <option value=2>2</option>
    <option value=3>3</option>
    <option value=4>4</option>
  </select>
</div>

https://plnkr.co/edit/R7QfJfy6m6IgHKL07tFI?p=preview