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
The difference between the high end and the low end of the range can be found by subtracting the low end from the high end.
High end of the range: 2.329×10^-2 cm per hour
Low end of the range: 6.849×10^-4 cm per hour
Difference = (2.329×10^-2) - (6.849×10^-4)
To subtract the numbers in scientific notation, we need to have the same exponent. Here, we can convert 6.849×10^-4 to scientific notation with the same exponent as 2.329×10^-2:
6.849×10^-4 = 6.849×10^-4 × 10^0 = 6.849×10^-4 × 10^(-2+2) = 6.849×10^-4 × 10^2 = 6.849×10^-2
Now, we can subtract the numbers:
Difference = (2.329×10^-2) - (6.849×10^-2)
To subtract, we subtract the coefficients (numbers in front) and keep the common exponent:
Difference = (2.329 - 6.849) × 10^-2
Difference = -4.52 × 10^-2
Therefore, the difference between the high end and the low end of the range is -4.52×10^-2 cm per hour.