Question

(a) an astronomers infrared telescope is able to detect radiation with a wavelength of $9.57 \times 10^{-5}$ meters. write this number in standard notation. (b) the diameter of pluto at its equator is approximately 2390 kilometers. write this number in scientific notation. (a) \boxed{} meters (b) \boxed{} kilometers

Explanation:

Step1: Convert \( 9.57 \times 10^{-5} \) to standard notation

To convert a number from scientific notation \( a \times 10^n \) to standard notation, if \( n \) is negative, we move the decimal point \( |n| \) places to the left. For \( 9.57 \times 10^{-5} \), \( n = -5 \), so we move the decimal point 5 places to the left.
\( 9.57 \times 10^{-5} = 0.0000957 \)

Step2: Convert 2390 to scientific notation

To convert a number to scientific notation, we write it as \( a \times 10^n \) where \( 1 \leq |a| < 10 \) and \( n \) is an integer. For 2390, we move the decimal point 3 places to the left to get \( a = 2.39 \), and \( n = 3 \) (since we moved the decimal 3 places to the left). So \( 2390 = 2.39 \times 10^3 \)

Answer:

(a) \( 0.0000957 \) meters
(b) \( 2.39 \times 10^3 \) kilometers