To find the difference between the high end and the low end of the range of hair growth rates, we need to subtract the lower rate from the higher rate.
The high end of the range is \( 2.329 \times 10^{-2} \) cm per hour, and the low end is \( 6.849 \times 10^{-4} \) cm per hour.
First, we need to express both numbers in the same format for easier subtraction. The high end can be rewritten in a similar power of ten as the low end:
\[ 2.329 \times 10^{-2} = 23.29 \times 10^{-3} \]
Now we can subtract:
\[ 23.29 \times 10^{-3} - 0.6849 \times 10^{-3} \]
To perform this subtraction, we align the numbers:
\[ 23.29 \times 10^{-3} - 0.6849 \times 10^{-3} = (23.29 - 0.6849) \times 10^{-3} = 22.6051 \times 10^{-3} \]
Now, we convert this result back to scientific notation by moving the decimal one place to the left:
\[ 22.6051 \times 10^{-3} = 2.26051 \times 10^{-2} \]
Thus, the difference between the high end and the low end of the range of hair growth rates is:
\[ \boxed{2.26051 \times 10^{-2}} \text{ cm per hour} \]
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