Question

1. dna is approximately 2.5 nm in length. if an average man is 5 ft 10 in. tall, how many dna molecules could be stacked to extend from the ground to the top of the head of an average man?

Explanation:

Step1: Convert man's height to nanometers

First, convert 5 ft 10 in to inches. 5 ft = 5×12 = 60 in, so 5 ft 10 in = 60 + 10=70 in. Since 1 in = 2.54 cm = 2.54×10⁷ nm, the height of the man in nm is \(h = 70\times2.54\times10^{7}\text{ nm}\).

Step2: Calculate the number of DNA molecules

Let the length of one - DNA molecule be \(l = 2.5\text{ nm}\). The number of DNA molecules \(n=\frac{h}{l}\). Substitute \(h = 70\times2.54\times10^{7}\text{ nm}\) and \(l = 2.5\text{ nm}\) into the formula: \(n=\frac{70\times2.54\times10^{7}}{2.5}\).
\[

$$\begin{align*} n&=\frac{70\times2.54\times10^{7}}{2.5}\\ &=\frac{70\times2.54}{2.5}\times10^{7}\\ &=\frac{177.8}{2.5}\times10^{7}\\ & = 71.12\times10^{7}\\ &=7.112\times 10^{8} \end{align*}$$

\]

Answer:

\(7.112\times 10^{8}\)