To find the difference between the high end and the low end of the hair growth rates expressed in scientific notation, you need to perform the subtraction:
- High end: \(2.329 \times 10^{-2}\) cm per hour
- Low end: \(6.849 \times 10^{-4}\) cm per hour
Before subtracting, we need to express both numbers with the same exponent. The high end (\(2.329 \times 10^{-2}\)) can be converted to the same exponent as the low end (\(10^{-4}\)).
To convert \(2.329 \times 10^{-2}\) to the \(10^{-4}\) exponent:
\[ 2.329 \times 10^{-2} = 2.329 \times 10^{-2} \times \frac{100}{100} = 2.329 \times \frac{100}{1} \times 10^{-4} = 232.9 \times 10^{-4} \]
Now we can subtract:
\[ 232.9 \times 10^{-4} - 6.849 \times 10^{-4} = (232.9 - 6.849) \times 10^{-4} \]
Calculating the subtraction:
\[ 232.9 - 6.849 = 226.051 \]
Now, we express \(226.051\) in scientific notation:
\[ 226.051 = 2.26051 \times 10^{2} \]
Now combine that with the \(10^{-4}\):
\[ 226.051 \times 10^{-4} = 2.26051 \times 10^{2} \times 10^{-4} = 2.26051 \times 10^{-2} \]
So, the final answer expressed in scientific notation is:
\[ \boxed{2.26051 \times 10^{-2}} \text{ cm per hour} \]