Question

suppose your hair grows at the rate 1/31 in. per day. find the rate at which it grows in nanometers per second. because the distance between atoms in a molecule is on the order of 0.1 nm, your answer suggests how rapidly layers of atoms are assembled in this protein synthesis. nm/s

Explanation:

Step1: Convert inches to meters

1 inch = 0.0254 meters. So, $\frac{1}{31}$ in. = $\frac{1}{31}\times0.0254$ m.

Step2: Convert meters to nanometers

1 m = $10^{9}$ nm. So, $\frac{1}{31}\times0.0254$ m = $\frac{1}{31}\times0.0254\times10^{9}$ nm.

Step3: Convert days to seconds

1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds. So 1 day = 24×60×60 s = 86400 s.

Step4: Calculate the rate in nm/s

The rate in nm/s is $\frac{\frac{1}{31}\times0.0254\times10^{9}}{86400}$ nm/s.
\[

$$\begin{align*} \frac{\frac{1}{31}\times0.0254\times10^{9}}{86400}&=\frac{0.0254\times10^{9}}{31\times86400}\\ &=\frac{2.54\times10^{7}}{31\times86400}\\ &=\frac{2.54\times10^{7}}{2678400}\\ &\approx9.48 \end{align*}$$

\]

Answer:

9.48 nm/s