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.
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To find the difference between the high end and the low end of the range, we subtract 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 = High end - Low end
Difference = (2.329 × 10^−2) - (6.849 × 10^−4)
To subtract these numbers, we need to rewrite the numbers with the same exponent of 10.
2.329 × 10^−2 = 0.02329 × 10^−2
6.849 × 10^−4 = 0.006849 × 10^−4
Difference = 0.02329 × 10^−2 - 0.006849 × 10^−4
Now, we can subtract the numbers:
Difference = 0.02329 × 10^−2 - 0.006849 × 10^−4
Difference = 0.02329 - 0.006849 × 10^(−2-4)
Difference = 0.02329 - 0.006849 × 10^(-6)
Difference = 0.02329 - 0.000006849
Now subtract the numbers:
Difference = 0.023283151 - 0.000006849
The difference between the high end and the low end of the range is approximately 0.023276302.
Expressed in scientific notation, this becomes 2.3276302 × 10^−2.
To find the difference between the high end and the low end of the range, we need to subtract the low end value from the high end value.
High end value = 2.329 × 10^−2 cm per hour
Low end value = 6.849 × 10^−4 cm per hour
To subtract these values, we can subtract the mantissas (the numbers multiplied by the powers of 10) and keep the same exponent:
(2.329 × 10^−2) - (6.849 × 10^−4)
To subtract the mantissas, we consider the numbers without the powers of 10:
2.329 - 6.849
This gives us -4.52
Now, to express this in scientific notation, we need to write it as a number between 1 and 10, multiplied by a power of 10. To do this, we can express -4.52 as -4.52 × 10^0:
-4.52 × 10^0
Therefore, the difference between the high end and the low end of the range is -4.52 × 10^0.
To find the difference between the high end and low end of the range, we subtract the low end from the high end:
2.329 × 10^−2 cm per hour - 6.849 × 10^−4 cm per hour
To subtract these numbers, we need to have the same exponent. To do this, we can express 6.849 × 10^−4 cm per hour in scientific notation as 6.849 × 10^−4 x 10^(2+2) = 6.849 × 10^−4 x 10^2 = 6.849 × 10^−2.
So, the difference between the high end and the low end of the range is:
(2.329 - 6.849) × 10^−2
Therefore, the difference between the high end and the low end of the range is 2.329 × 10^−2 - 6.849 × 10^−2 = (2.329 - 6.849) × 10^−2 = -4.520 × 10^−2.
I apologize for the confusion. Let me re-calculate.
The low end of the range is 6.849 × 10^(-4) cm per hour.
The high end of the range is 2.329 × 10^(-2) cm per hour.
To find the difference, we subtract the low end from the high end:
(2.329 × 10^(-2)) - (6.849 × 10^(-4))
To subtract these numbers, we need to have the same exponent, which is 10^(-4) in this case.
Moving the decimal point in 2.329 two positions to the left, we get: 0.02329.
So the difference between the high end and low end of the range is:
(0.02329 - 0.0006849) × 10^(-4)
Subtracting the numbers, we get: 0.0226051 × 10^(-4).
In scientific notation, this can be expressed as:
2.26051 × 10^(-5)