This is a unit conversion problem. In order to get the number of DNA molecules, the height of the man should first be converted into nm. It would require multiple steps to do this.
For the provided solution, the following conversion factors are used:
12 in = 1 foot
1 in = 2.54 cm
1 m = 100 cm
1 m = 10⁹ nm
[tex]height = 5 \ ft \times \frac{12 \ in}{1 \ ft} = 60 \ in[/tex]
The height is 5 ft 10 inches. 5 feet is equivalent to 60 inches. Therefore, the average man is 70 inches tall.
Since the DNA molecules are measured in nanometers, it is necessary to determine how tall the man is in nanometers.
[tex]height \ in \ nm \ = 70 \ in \times \frac{2.54 \ cm}{1 \ in} \times \frac{1 \ m}{100 \ cm} \times \frac{10^9 \ nm}{1 \ m}\\\\\boxed {height \ in \ nm \ = 1.778 \times 10^{9} \ nm}[/tex]
To find the number of DNA molecules it would be required to calculate how many 2.5 nm molecules could be stacked together to a total height of 1.778 × 10⁹ nm.
[tex]number \ of \ DNA \ molecules \ = 1.778 \times 10^{9} \ nm \ \times \frac{1 \ molecule}{2.5 \ nm} \\\\\boxed {number \ of \ DNA \ molecules \ = 7.112 \times 10^8 \ molecules}[/tex]
Since the least number of significant figures in the given is 1, the answer should have one significant figure also. Hence, the final answer is:
[tex]\boxed {\boxed {number \ of \ DNA \ molecules \ = 7 \times 10^{8} \ molecules}}[/tex]
Keywords: DNA, conversion
