Final answer:
The numbers 3.4 nm and 0.34 nm are critical for understanding the double helical structure of DNA, indicating the distance of a complete helical turn and the spacing between base pairs, respectively.
Step-by-step explanation:
The numbers 3.4 nm and 0.34 nm obtained from the analysis of DNA by Rosalind Franklin and Maurice Wilkins using X-ray diffraction are significant because they helped James Watson and Francis Crick to deduce the structure of DNA. The 3.4 nm measurement represents the pitch of the DNA helix, indicating that there is one complete turn of the helix at every 3.4 nm. Meanwhile, the 0.34 nm measurement is the distance between successive nucleotide pairs within the DNA structure, indicating that there are 10 nucleotide pairs, or base pairs, for every complete turn of the helix. This contributes to the understanding that DNA has a double helical structure, with the bases stacked 0.34 nm apart, and that it completes a turn every 3.4 nm.