Why is the target truncated?
Target is stored in block header (it's called Bits), and it takes only 4 bytes. We derive target 256-bit value from these 32 bits. That's why it is getting truncated.

There is no need to store all 256 bits, or even 224 bits (if we assume first 4 bytes are zero). We don't need such precision.

You can read in wiki, how target is getting calculated from Bits.

You can also check my answer here, with example: 
How does difficulty is defined for block &#39;55798&#39;?