What is the wavelength of 9.517 × 10^−6 meters in scientific notation?
Understand the Problem
The question requires converting the wavelength of 9.517 × 10^−6 meters into standard scientific notation and addressing the diameter of Jupiter in kilometers.
Answer
$9.517 \times 10^{-9}$ kilometers.
Answer for screen readers
The wavelength in scientific notation is $9.517 \times 10^{-9}$ kilometers.
Steps to Solve
- Convert Wavelength to Standard Scientific Notation
The given wavelength is $9.517 \times 10^{-6}$ meters, which is already in scientific notation.
- Convert the Wavelength to Kilometers
To convert from meters to kilometers, we use the conversion factor:
$$ 1 \text{ kilometer} = 1000 \text{ meters} $$
Thus, we need to divide the wavelength by 1000:
$$ 9.517 \times 10^{-6} \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 9.517 \times 10^{-6} \times 10^{-3} \text{ km} = 9.517 \times 10^{-9} \text{ km} $$
- Final Answer in Scientific Notation
The wavelength in kilometers is therefore expressed as $9.517 \times 10^{-9}$ kilometers.
The wavelength in scientific notation is $9.517 \times 10^{-9}$ kilometers.
More Information
This conversion is important in astronomy since wavelengths are often measured in meters, but for many astronomical applications, it's useful to express them in kilometers.
Tips
- Misunderstanding the conversion factor; remember that $1 \text{ km} = 1000 \text{ m}$, so you need to divide.
- Not expressing the final answer in scientific notation correctly.
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