Prevent insert record if ASP.Net DropDownList is empty using C#

I tried to prevent insert record if the dropdownList is empty but the record still inserts on empty DropdownList.

How can prevent insert when dropdown control is empty?

MY HTML and CODE

<asp:DropDownList ID="productdropdown" runat="server" CssClass="form-control" AutoPostBack="true" 
    OnSelectedIndexChanged="productdropdown_SelectedIndexChanged">
    <asp:ListItem Selected="True" Text="Select a number"></asp:ListItem>
    <asp:ListItem Value="Chhose 1"></asp:ListItem>
    <asp:ListItem Value="Choose 2"></asp:ListItem>
</asp:DropDownList>
<asp:Button runat="server" Class="btn btn-primary" Text="insert number"/>

CODE

protected void ButtonSubmit_Click(object sender, EventArgs e)
{
    if (productdropdown.SelectedValue != "")
    {
        //my insert code
    }
    else
    {
        ClientScript.RegisterClientScriptBlock(this.GetType(), "", "alert('Please Select a number')", true);
    }
}