Question

Question
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 lower growth rate from the higher growth rate:

- High end: \( 2.329 \times 10^{-2} \) cm per hour
- Low end: \( 6.849 \times 10^{-4} \) cm per hour

We can perform the subtraction as follows:

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

First, we need to express both numbers with the same exponent. We can convert \( 2.329 \times 10^{-2} \) to an equivalent 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:

\[
232.9 \times 10^{-4} - 6.849 \times 10^{-4} = (232.9 - 6.849) \times 10^{-4}
\]

Calculating \( 232.9 - 6.849 \):

\[
232.9 - 6.849 = 226.051
\]

Now we have:

\[
226.051 \times 10^{-4}
\]

To express this in scientific notation, we can write \( 226.051 \) as \( 2.26051 \times 10^{2} \):

\[
226.051 \times 10^{-4} = 2.26051 \times 10^{2} \times 10^{-4} = 2.26051 \times 10^{-2}
\]

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

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