To find the difference between the high end and the low end of the range of human hair growth rates:
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Identify the growth rates:
- Low end: \(6.849 \times 10^{-4}\) cm per hour
- High end: \(2.329 \times 10^{-2}\) cm per hour
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Convert both numbers to the same exponent for easy subtraction. The low end can be rewritten:
\[ 6.849 \times 10^{-4} = 0.0006849 \text{ cm per hour} \]
And the high end can be expressed as:
\[ 2.329 \times 10^{-2} = 0.02329 \text{ cm per hour} \]
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Now, we can convert the low end to match the exponent of the high end:
\[ 6.849 \times 10^{-4} = 0.0006849 = 0.00006849 \times 10^{-2} = 6.849 \times 10^{-4} \times \frac{10^{2}}{10^{2}} = 684.9 \times 10^{-6} \]
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Now, subtract the two values:
\[ 2.329 \times 10^{-2} - 6.849 \times 10^{-4} \]
Converting \(2.329 \times 10^{-2}\) into a comparable format:
\[ 2.329 \times 10^{-2} = 23.29 \times 10^{-3} \]
Now, we rewrite the low end in terms of the same exponent:
- \(6.849 \times 10^{-4} = 0.6849 \times 10^{-3}\)
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Now we can subtract:
\[ (23.29 \times 10^{-3}) - (0.6849 \times 10^{-3}) = (23.29 - 0.6849) \times 10^{-3} = 22.6051 \times 10^{-3} \]
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Now, convert it back into scientific notation:
\[ 22.6051 \times 10^{-3} = 2.26051 \times 10^{-2} \]
So the difference between the high end and the low end of the hair growth rate is:
\[ \boxed{2.26051 \times 10^{-2}} \text{ cm per hour} \]