Final answer:
Nucleosome formation reduces the length of DNA to about one-seventh of its original length. The further coiling into a 30-nm chromatin fiber compacts the chromosome to about 50 times shorter than its extended form.
Step-by-step explanation:
Nucleosome formation compacts the DNA into approximately one-seventh of its original length. During this first level of DNA compaction, stretches of the DNA double helix are wrapped around a core of eight histone proteins, forming what is known as a nucleosome. These nucleosomes, interspersed by linker DNA, stack compactly onto each other, leading to a significant reduction in the length of DNA.
Subsequently, nucleosomes and linker DNA coil into a 30-nm chromatin fiber, condensing the chromosome approximately 50 times shorter than its fully extended form. This hierarchical structuring is essential for fitting the lengthy eukaryotic DNA within the confines of a cell nucleus, which necessitates efficient and dense packaging.