Questions: The diameter of Neptune at its equator is approximately 4.95 × 10^4 kilometers. Write this number in standard notation. An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.0000957 meters. Write this number in scientific notation.

The diameter of Neptune at its equator is approximately 4.95 × 10^4 kilometers. Write this number in standard notation. An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.0000957 meters. Write this number in scientific notation.
Transcript text: The diameter of Neptune at its equator is approximately $4.95 \times 10^{4}$ kilometers. Write this number in standard notation. An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.0000957 meters. Write this number in scientific notation.
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Solution

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Solution Steps

Step 1: Converting Scientific Notation to Standard Notation

To convert the diameter of Neptune from scientific notation to standard notation, we start with the given value: \[ 4.95 \times 10^{4} \] This means we move the decimal point 4 places to the right: \[ 4.95 \rightarrow 49500 \]

Step 2: Converting Standard Notation to Scientific Notation

To convert the wavelength from standard notation to scientific notation, we start with the given value: \[ 0.0000957 \] We need to express this number as a product of a number between 1 and 10 and a power of 10. We move the decimal point 5 places to the right: \[ 0.0000957 = 9.57 \times 10^{-5} \]

Final Answer

The diameter of Neptune in standard notation is: \[ \boxed{49500 \text{ kilometers}} \]

The wavelength in scientific notation is: \[ \boxed{9.57 \times 10^{-5} \text{ meters}} \]

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