Change the img tag to:
<img src="picture01.jpg" alt="" />
<img src="http://mysite.com/picture01.jpg" alt="picture 01" />
where mysite.com is your fully qualified domain name.
You may or may not need www. here, like:
<img src="http://www.mysite.com/picture01.jpg" alt="use alt text" />
The alt text is a short piece of text that describes the image for browsers that do not show images.
It is also further recommended to use WordPress to get the home url, so that anything hard coded is not affected by a domain name change.
<?php get_home_url(); ?>
<img src="<?php get_home_url(); ?>/picture01.jpg" alt="use alt text" />
The trailing slash may or may not be required and also please note that image files are not typically located in the root. Use an FTP client, such as FileZilla to find this file picture01.jpg and for quick uploads, site backup, and site maintenance.