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 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.
To find the difference between the high end and low end of the range, we 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
Difference = (2.329×10^-²) - (6.849×10^-⁴)
To subtract these two numbers, we need to make sure they have the same exponent. We can do this by converting the low end to the same exponent as the high end.
6.849×10^-⁴ = 6.849×10^-⁴ * 10^-² * 10² = 6.849×10^-⁶
Now we can subtract:
Difference = (2.329×10^-²) - (6.849×10^-⁶)
To subtract, we subtract the decimal parts and keep the same exponent:
Difference = 2.329×10^-² - 6.849×10^-⁶ = 2.328993151×10^-² - 6.8485×10^-⁶
Therefore, the difference between the high end and low end of the range is 2.328993151×10^-² - 6.8485×10^-⁶.
To find the difference between the high end and low end of the range, we 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
Subtracting the low end from the high end:
(2.329×10^-²) - (6.849×10^-⁴)
To subtract the two quantities in scientific notation, their exponents must be the same. The exponents can be made the same by moving the decimal point. In this case, we can move the decimal point 2 places to the right in the low end to match it with the high end.
(2.329×10^-²) - (0.006849×10^-²)
Now that the exponents are the same, we can subtract the two quantities:
(2.329 - 0.006849) × 10^-²
Calculating the difference:
2.322151 × 10^-²
Therefore, the difference between the high end and the low end of the range, expressed in scientific notation, is 2.322151 × 10^-².