Question: I have dual boot with Ubuntu 12.04 and Windows 7, and I would like to upgrade Ubuntu to 14.04 but still retain my windows 7, help! I have a DVD with the ubuntu 14.04 ISO

Answer: 
If you copy a partition with `dd`, the output file will be as big as the partition. `dd` does a physical copy of the disc, it has no knowledge of blank or used space. 

If you compress the result file you will save a lot of space, though, given that blank space will compress away very well (beware, this is going to be computationally *very* heavy). You can even compress the output of `dd` on the fly, with something on the line of `dd if=/dev/sdaX | gzip -c > compressed_file.gz`. 

really important:
-----------------

> 
> Moreover, you **cannot** (never) do a `dd` on a live (mounted)
>  partition, the data recorded will be totally inconsistent and
>  absolutely not useful for a backup. Think about it: blocks of data are
>  continually allocated, moved and deleted; is like shooting a photo
>  with long exposure time to a moving target.
> 
> 
> To copy the partition with `dd` you must boot from a different one -
>  live USB or whatever.
> 
> 
> 

What would I do to solve the problem at hand (notice, only generic instruction because you need to know what you are doing)

*First option* buy Norton Ghost, or explore the opensource options: [partimage](http://www.partimage.org/Main_Page) and [clonezilla](http://clonezilla.org/) (never tested myself). 

*Second option* do it manually: 

1. create an extra partition for backups, call it /dev/sdX (or use a common data partition, whatever).
2. to backup:

	* boot with live usb
	* mount the real root partition in /real
	* mount the extra partition in /extra
	* do a big tar, on the line of `(cd /real && tar cvf /extra/mybck.tar.gz)`
3. to restore 

	* boot with live usb
	* mount the real root partition in /real
	* mount the extra partition in /extra
	* restore, on the line of `(cd /real && tar xvpf /extra/mybck.tar.gz)`, beware of the `p` option to preserve metadata
	* chroot in /real
	* update grub or the bootloader you are using

You can substitute `tar` with your preferred archiver, just be sure it will respect ownership/mode of files. `rsync` is worth exploring.
DD probably isn't the right tool to do a backup. As Rmano said, it's making a direct copy of /dev/sda4 (probably to /dev/sda4). 

His answer is spot on.

Check out rsync for doing backups.