Question

Human hair grows at a rate of about 6.849 x 10-4 cm per hour to 2.329 x 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. (1 point)

cm per hour

Answer 1

To find the difference between the high end and the low end of the range, we can subtract the lower growth rate from the upper growth rate.

Given:
- Lower growth rate: \( 6.849 \times 10^{-4} \) cm/hour
- Upper growth rate: \( 2.329 \times 10^{-2} \) cm/hour

First, we can convert the upper growth rate to the same power of ten as the lower growth rate for easier subtraction:

\[
2.329 \times 10^{-2} \, \text{cm/hour} = 2.329 \times 10^{-2} \times \frac{10^2}{10^2} = 232.9 \times 10^{0} \, \text{cm/hour} = 232.9
\]

Now we want to convert \( 6.849 \times 10^{-4} \) to a decimal for easier calculation. It is already in scientific notation, representing:

\[
0.0006849
\]

Now perform the subtraction:

\[
= 2.329 \times 10^{-2} \, \text{cm/hour} - 6.849 \times 10^{-4} \, \text{cm/hour}
\]
\[
= 0.02329 - 0.0006849
\]

Aligning the decimals for subtraction:

\[
\begin{array}{r}
0.0232900 \\
-0.0006849 \\
\hline
0.0226051
\end{array}
\]

Converting \( 0.0226051 \) back into scientific notation:

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

Thus, the difference between the high end and the low end of the range is:

\[
\boxed{2.26051 \times 10^{-2}} \, \text{cm per hour}
\]