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 calculated by subtracting the low end from the high end.
High end rate = 2.329×10^−2 cm per hour
Low end rate = 6.849×10^−4 cm per hour
Difference = High end rate - Low end rate
Difference = (2.329×10^−2) - (6.849×10^−4)
Difference = 2.329×10^−2 - 6.849×10^−4
To subtract these numbers, they need to be in the same scientific notation. We will convert the low end rate to the same power of 10 as the high end rate.
6.849×10^−4 = 0.0006849 ×10^−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 powers of 10, the numbers need to be in the same power of 10. We can rewrite the high end rate as:
2.329×10^-2 = 0.02329 ×10^0 = 0.02329 ×10^-2 ×10^2 = 2.329×10^0
Now we can subtract the numbers:
Difference = 2.329×10^0 - 6.849×10^-2
Given that we are asked to express the answer in scientific notation, we need to convert the result to scientific notation:
Difference = 2.329×10^0 - 6.849×10^-2 = 2.329 - 0.06849 = 2.26051
To express this result in scientific notation, we shift the decimal point to have a single nonzero digit in front of it:
Difference = 2.26051 = 2.26051 × 10^0 = 2.26051 × 10^0
Therefore, the difference between the high end and the low end of the range is 2.26051 × 10^0, which can be written in scientific notation as 2.26051.
To find the difference between the high end and the low end of the range, we simply subtract the low end from the high end.
High end: 2.329×10^−2 cm per hour
Low end: 6.849×10^−4 cm per hour
Difference = High end - Low end
= (2.329×10^−2) - (6.849×10^−4)
To perform the subtraction, we need to make sure the exponents of 10 are the same.
We can rewrite the low end as:
= (6.849×10^−4) * (1×10^0)
Now we subtract:
= (2.329×10^−2) - (6.849×10^−4) * (1×10^0)
= 2.329×10^−2 - 6.849×10^−4
Now, since the exponents of 10 are the same, we can subtract the coefficients:
= 2.329 - 6.849×10^−4
To express the answer in scientific notation, we need to bring the decimal point to a place between 1 and 10. Therefore, we can rewrite it as:
= 2.329 - 0.0006849×10^1
= 2.329 - 0.006849
= 2.322151
In scientific notation, this is equal to:
= 2.322151×10^0
Therefore, the difference between the high end and the low end of the range is approximately 2.322151×10^0 cm per hour.
To find the difference between the high end and the low end of the range, we subtract the low end value from the high end value.
High end: 2.329×10^−2 cm per hour
Low end: 6.849×10^−4 cm per hour
Subtracting the low end from the high end:
2.329×10^−2 cm per hour - 6.849×10^−4 cm per hour
To subtract these values, we need to ensure that the exponents of 10 are the same.
Since the exponents are different (−2 and −4), we can convert the low end value to the same exponent as the high end value.
To achieve this, we can multiply the low end value by 10^(-2+4), which simplifies to 10^2.
(6.849×10^−4 cm per hour) * (10^2)
Simplifying:
6.849×10^(-4+2)
6.849×10^(-2)
Now that both values have the same exponent, we can subtract them:
(2.329×10^−2 cm per hour) - (6.849×10^−2 cm per hour)
= -4.52×10^(-2) cm per hour
Therefore, the difference between the high end and the low end of the range is -4.52×10^(-2) cm per hour.