Determine which ratio is larger: the size (diameter) of Earth to a human, or the size of a human compared to a white blood cell? How would you figure this out (rough math is OK).

To determine which ratio is larger — the size of Earth to a human, or the size of a human to a white blood cell — we can estimate the sizes involved and compare the ratios.

Size of Earth to a Human

According to NASA, the diameter of the Earth is approximately 12,756 km. Therefore:

[tex]\boxed{\begin{array}{l}\textsf{Diameter of Earth $\approx$ 12,756 kilometers = 12,756,000 meters}\\\\\textsf{Average height of a human $\approx$ 1.7 meters}\end{array}}[/tex]

So, the ratio of the diameter of Earth to a human is:

[tex]\textsf{Ratio}=\dfrac{\textsf{Diameter of Earth}}{\textsf{Height of a human}} \\\\\\\textsf{Ratio}= \dfrac{12\:756\:000 \textsf{ m}}{1.7 \textsf{ m}} \\\\\\ \textsf{Ratio}\approx \dfrac{7\:503\:529}{1} \\\\\\ \textsf{Ratio}\approx 7\:503\:529: 1[/tex]

This means that the diameter of the Earth is approximately 7,503,529 times the height of a human.

Size of a Human to a White Blood Cell

According to B10NUMB3R5 at Harvard University, the usual dimensions of a white blood cell on blood smear is 10 µm - 20 µm. Therefore:

[tex]\boxed{\begin{array}{l}\textsf{Average height of a human $\approx$ 1.7 meters} \\\\\textsf{Average diameter of a white blood cell $\approx$ 15 $\sf \mu m$ = 0.000015 meters}\end{array}}[/tex]

So, the ratio of the height of a human to the diameter of a white blood cell is:

[tex]\textsf{Ratio}=\dfrac{\textsf{Height of a human}}{\textsf{Diameter of a white blood cell}} \\\\\\\textsf{Ratio}= \dfrac{1.7 \textsf{ m}}{0.000\:015 \textsf{ m}} \\\\\\ \textsf{Ratio}\approx \dfrac{113\:333}{1} \\\\\\ \textsf{Ratio}\approx 113\:333:1[/tex]

This means that the height of a human is approximately 113,333 times the diameter of a white blood cell.

Conclusion

The ratio of the size of Earth to a human is significantly larger (approximately 66 times larger) than the ratio of a human to a white blood cell.