Question

answer the following.
(a) an astronomer’s infrared telescope is able to detect radiation with a wavelength of \\(2.68 \times 10^{-5}\\) meters. write this number in standard notation.
(b) the diameter of mars at its equator is approximately 6790 kilometers. write this number in scientific notation.
(a) \\(\square\\) meters
(b) \\(\square\\) kilometers

Explanation:

Step1: Convert scientific to standard notation

A negative exponent means moving the decimal left 5 places: $2.68 \times 10^{-5} = 0.0000268$

Step2: Convert standard to scientific notation

Move decimal left 3 places to get a 1-digit coefficient: $6790 = 6.79 \times 10^{3}$

Answer:

(a) 0.0000268 meters
(b) $6.79 \times 10^{3}$ kilometers