Human hair grows at a rate of about 6.849 × 10 − 4 cm per hour to 2.329 × 10 − 2 cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation. Do not round your answer.

Answer 1

To find the difference between the high end and the low end of the hair growth rate, we need to subtract the low end from the high end.

The high end of the range is \(2.329 \times 10^{-2}\) cm/hour and the low end is \(6.849 \times 10^{-4}\) cm/hour.

Now let's first express both numbers in a common format to simplify the subtraction. We'll rewrite the low end to have the same exponent as the high end.

\[ 6.849 \times 10^{-4} = 0.0006849 \text{ cm/hour} \]

Next, we need to express \(2.329 \times 10^{-2}\) with a similar exponent:

\[ 2.329 \times 10^{-2} = 0.02329 \text{ cm/hour} \]

Now we can perform the subtraction:

\[ 2.329 \times 10^{-2} - 6.849 \times 10^{-4} = 0.02329 - 0.0006849 \]

Calculating the above:

\[ 0.02329 - 0.0006849 = 0.0226051 \text{ cm/hour} \]

Next, to express this result in scientific notation, we can convert \(0.0226051\) to scientific notation:

\[ 0.0226051 = 2.26051 \times 10^{-2} \]

Thus, the difference between the high end and the low end of the range, expressed in scientific notation, is:

\[ \boxed{2.26051 \times 10^{-2}} \]