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

The difference between the high end and the low end of the range can be calculated by subtracting the low end value from the high end value:

(2.329×10^-² cm/hour) - (6.849×10^-⁴ cm/hour)

To subtract these values, we need to make sure both terms have the same exponent. In this case, we can convert the low end value to scientific notation with the same exponent as the high end value:

(2.329×10^-² cm/hour) - (6.849×10^-⁴ cm/hour)
= (0.02329×10^-1 cm/hour) - (6.849×10^-⁴ cm/hour)

Now the exponents match, so we can subtract the values:

(0.02329×10^-1 cm/hour) - (6.849×10^-⁴ cm/hour)
= 0.02329×10^-1 - 6.849×10^-⁴

Since both terms have the same base (10), we can subtract their coefficients:

= 0.02329 - 6.849×10^-⁴

The result is 0.02329 minus a small value (6.849×10^-⁴), which is still 0.02329 since the small value is negligible.

Therefore, the difference between the high end and the low end of the range is 0.02329 expressed in scientific notation: 2.329×10^-².