Question

The number of cells in an average-sized adult human is on the order of 10^14 cells. Use this information, and the estimate that the length of DNA contained in each cell is 2 meters, to do the following calculations. Show all of your work with units.
Some conversions that might be useful: 1 meter=6.21 X 10^-4 miles Average Distance from Earth to the Sun=93,000,000 miles= 9.3 X 10^7 miles
Over how many miles would the total DNA from the average human stretch?
How many times would the total DNA from the average human stretch from Earth to the Sun and back?

Answer 1

IF:
Number of cells: $C = 10^{14}$
DNA lenght: $D = 2m = 12.42 * 10^{-4} mi$
Distance from Earth to Sun: $ES=93000000 mi = 9.3* 10^{7}mi$

Then:
a) Over how many miles would the total DNA from the average human stretch?
The answer is product of multiplication of the number of cells (C) and the DNA length (D):
Total DNA: $T = C*D$
              ⇒ $T = 10^{14}*12.42* 10^{-4} mi$
              ⇒ $T = 12.42* 10^{14-4} mi$
              ⇒ $T = 12.42* 10^{10} mi$
The total DNA from the average human will stretch $12.42* 10^{10} mi$

b) How many times would the total DNA from the average human stretch from Earth to the Sun and back?
The answer is concluded from the ratio of the total DNA length (T) and the twice (because of stretch to the Sun and back, thus, two directions) of distance from Earth to the Sun (ES) and :
Ratio: $R= \frac{T}{2*ES}$
      ⇒ $R = \frac{12.42* 10^{10}mi }{2*(9.3* 10^{7}mi)}$
      ⇒ $R = \frac{12.42* 10^{10}}{18.6*10^{7}}$
      ⇒ $R = 0.6677* 10^{10-7}$
      ⇒ $R = 0.6677* 10^{3}$
      ⇒ [tex]R = 667.7
Thus, 667,7 times will the total DNA from the average human stretch from Earth to the Sun and back.