Subtract Numbers in Scientific Notation Practice

Question

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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 range, we will subtract the lower value from the higher value:

1. Identify the two values:

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

2. Before subtracting, we need to express them with the same exponent. The high end is at \( 10^{-2} \), while the low end is at \( 10^{-4} \). We can convert the low end to \( 10^{-2} \) for easier subtraction.

   \[ 6.849 \times 10^{-4} = 0.06849 \times 10^{-2} \]

3. Now we can perform the subtraction: \[ 2.329 \times 10^{-2} - 0.06849 \times 10^{-2} = (2.329 - 0.06849) \times 10^{-2} \] \[ = 2.26051 \times 10^{-2} \]

4. Expressing the difference in scientific notation gives: \[ 2.26051 \times 10^{-2} \]

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

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