Question

answer the following. (a) an astronomers infrared telescope is able to detect radiation with a wavelength of 1.96×10^(-4) meters. write this number in standard notation. (b) the diameter of saturn at its equator is approximately 121,000 kilometers. write this number in scientific notation.

Explanation:

Step1: Convert scientific - notation to standard notation

The scientific - notation is $a\times10^{n}$, where $1\leq a<10$ and $n$ is an integer. For $1.96\times 10^{-4}$ meters, when $n=- 4$, we move the decimal point 4 places to the left. So, $1.96\times 10^{-4}=0.000196$ meters.

Step2: Convert kilometers to scientific - notation

The diameter of Saturn is 121000 kilometers. To write it in scientific - notation, we move the decimal point until we have a number between 1 and 10. We move the decimal point 5 places to the left, so $121000 = 1.21\times10^{5}$ kilometers.

Answer:

(a) $0.000196$ meters
(b) $1.21\times 10^{5}$ kilometers