Suppose your hair grows at the rate $1/32$ 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 $0.1\mathrm{nm}$, your answer suggests how rapidly layers of atoms are assembled in this protein synthesis.

Key Concepts: Unit Conversion, Nanometers, Seconds, Division, Multiplication Explanation: To convert from inches to nanometers, we must multiply by $2.54\times 10^7$ (number of nanometers in an inch). To convert from days to seconds, we must multiply by 86400 (number of seconds in a day). So, we have:\n $\text{Rate of hair growth}=\frac{1}{32}\text{ in/day}\times 2.54\times 10^7\text{ nm/in}\times \frac{1}{86400}\text{ day/s}$\n After simplifying, we get:\n $\text{Rate of hair growth}=\frac{79}{2211840}\text{ nm/s}\approx 3.56\times 10^{-5}\text{ nm/s}$ Step by Step Solution: Step 1. Convert inches to nanometers by multiplying by 2.54E+7 Step 2. Convert days to seconds by multiplying by 86400 Step 3. Multiply the two conversion factors and divide by the given value to get the rate of hair growth in nanometers per second. Final Answer: The rate at which the hair grows in nanometers per second is approximately 3.56E-5 nm/s.