Questions: Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 5.32 × 10^-5 meters. Write this number in standard notation. (b) The diameter of Neptune at its equator is approximately 49,500 kilometers. Write this number in scientific notation.

Answer the following.
(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 5.32 × 10^-5 meters. Write this number in standard notation.
(b) The diameter of Neptune at its equator is approximately 49,500 kilometers. Write this number in scientific notation.

Transcript text: Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of $5.32 \times 10^{-5}$ meters. Write this number in standard notation. (b) The diameter of Neptune at its equator is approximately 49,500 kilometers. Write this number in scientific notation.

Solution

Solution Steps

Solution Approach

(a) To convert the given wavelength from scientific notation to standard notation, we need to move the decimal point 5 places to the left. (b) To convert the diameter of Neptune from standard notation to scientific notation, we need to express the number as a product of a number between 1 and 10 and a power of 10.

Step 1: Convert Wavelength to Standard Notation

The given wavelength is $ 5.32 \times 10^{-5} $ meters. In standard notation, this is expressed as: \[ wavelength = 5.32e-05 \text{ meters} \]

Step 2: Convert Diameter to Scientific Notation

The diameter of Neptune is approximately $ 49,500 $ kilometers. To express this in scientific notation, we write: \[ diameter = 4.95 \times 10^{4} \text{ kilometers} \]