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 you answer.

To find the difference between the high end and low end of the hair growth rate, we will subtract the lower rate from the higher rate.

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

Let's perform the subtraction step by step:

1. Convert \(2.329 \times 10^{-2}\) to a standard form for easier subtraction: \[ 2.329 \times 10^{-2} = 0.02329 \text{ cm/hour} \]

2. Convert \(6.849 \times 10^{-4}\) to a standard form as well: \[ 6.849 \times 10^{-4} = 0.0006849 \text{ cm/hour} \]

3. Now we will subtract: \[ 0.02329 - 0.0006849 = 0.0226051 \]

4. Finally, we convert \(0.0226051\) back to scientific notation: \[ 0.0226051 = 2.26051 \times 10^{-2} \]

Thus, the difference between the high end and low end of the hair growth rate expressed in scientific notation is: \[ \boxed{2.26051 \times 10^{-2}} \]

Find 0.078 - (5.2 x 10^-3). Express your answer in scientific notation. Do not round your answer/

To subtract \(5.2 \times 10^{-3}\) from \(0.078\), we first need to express both numbers in a suitable form for easier calculation.

1. Convert \(0.078\) to scientific notation: \[ 0.078 = 7.8 \times 10^{-2} \]

2. Next, we convert \(5.2 \times 10^{-3}\) to the same exponent of \(10^{-2}\) for compatibility: \[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \]

3. Now we can rewrite the subtraction: \[ 7.8 \times 10^{-2} - 0.052 \times 10^{-2} = (7.8 - 0.052) \times 10^{-2} \]

4. Perform the subtraction: \[ 7.8 - 0.052 = 7.748 \]

5. Now, express \(7.748\) in scientific notation: \[ 7.748 \times 10^{-2} \]

Thus, the result of the subtraction \(0.078 - (5.2 \times 10^{-3})\) in scientific notation is: \[ \boxed{7.748 \times 10^{-2}} \]

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Let’s carefully go through the steps to find \(0.078 - (5.2 \times 10^{-3})\) and express the answer in scientific notation.

Step 1: Convert the numbers for easier calculation.

1. We already have \(5.2 \times 10^{-3}\) in scientific notation. We will convert \(0.078\) to scientific notation: \[ 0.078 = 7.8 \times 10^{-2} \]

Step 2: Convert \(5.2 \times 10^{-3}\) to match the exponent in \(7.8 \times 10^{-2}\).

To do this, we can express \(5.2 \times 10^{-3}\) in terms of \(10^{-2}\):

• We know that: \[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \] because: \[ 0.052 = 5.2 \div 10 = 5.2 \times 10^{-1} \]

Step 3: Now, perform the subtraction:

We can now rewrite \(0.078 - (5.2 \times 10^{-3})\) as: \[ (7.8 \times 10^{-2}) - (0.052 \times 10^{-2}) = (7.8 - 0.052) \times 10^{-2} \]

Step 4: Calculate \(7.8 - 0.052\): \[ 7.8 - 0.052 = 7.748 \]

Step 5: Write the result in scientific notation:

Now we have: \[ 7.748 \times 10^{-2} \]

Thus the answer in scientific notation is: \[ \boxed{7.748 \times 10^{-2}} \]

Note: If you want to be precise, \(0.078\) (which is \(7.8 \times 10^{-2}\)) and \(5.2 \times 10^{-3}\) were converted to the same exponent before performing the subtraction. The answer given above is still valid. If you were looking for a different step or concept, please clarify for further assistance!