To find the difference between the high end and the low end of the hair growth rate, we can subtract the low end from the high end.
The high end of the rate is \( 2.329 \times 10^{-2} \) cm per hour, and the low end is \( 6.849 \times 10^{-4} \) cm per hour.
First, we convert both numbers to have the same exponent for easier subtraction:
- The high end is \( 2.329 \times 10^{-2} \) cm per hour, which is already in the form we need.
- The low end can be converted as follows:
\[ 6.849 \times 10^{-4} = 0.0006849 = 0.00006849 \times 10^{-2} \]
Now we can perform the subtraction:
\[ 2.329 \times 10^{-2} - 0.0006849 \times 10^{-2} = 2.329 \times 10^{-2} - 0.00006849 \times 10^{-2} \]
Convert \( 0.00006849 \times 10^{-2} \) to scientific notation:
\[ 0.00006849 \times 10^{-2} = 6.849 \times 10^{-4} \rightarrow \text{from previous calculation} \]
Now, we proceed with the actual subtraction:
\[ = (2.329 - 0.0006849) \times 10^{-2} = 2.329 - 0.0006849 \approx 2.3283151 \]
Now we express this in scientific notation:
\[ 2.3283151 \times 10^{-2} \]
So, the difference between the high end and the low end of the range is:
\[ \boxed{2.3283151 \times 10^{-2}} \text{ cm per hour} \]