To find the difference between the high end and the low end of the hair growth rates, we need to subtract the lower growth rate from the higher growth rate.
The high end growth rate is \( 2.329 \times 10^{-2} \) cm per hour, and the low end growth rate is \( 6.849 \times 10^{-4} \) cm per hour.
First, we can express both numbers in the same power of ten for easier subtraction.
Convert \( 2.329 \times 10^{-2} \) into a form with \( 10^{-4} \): \[ 2.329 \times 10^{-2} = 2.329 \times 10^{-2} \times \frac{100}{100} = 232.9 \times 10^{-4} \]
Now, we can subtract: \[ \text{Difference} = 232.9 \times 10^{-4} - 6.849 \times 10^{-4} \] This gives: \[ \text{Difference} = (232.9 - 6.849) \times 10^{-4} = 226.051 \times 10^{-4} \]
Now we need to express \( 226.051 \times 10^{-4} \) in scientific notation. To do this, we move the decimal point two places to the left: \[ 226.051 \times 10^{-4} = 2.26051 \times 10^{-2} \]
So, the final answer expressing the difference between the high end and low end of the range in scientific notation is: \[ \boxed{2.26051 \times 10^{-2}} , \text{cm per hour} \]
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