Question

answer the following. (a) the diameter of saturn at its equator is approximately 1.21×10^5 kilometers. write this number in standard notation. (b) an astronomers infrared telescope is able to detect radiation with a wavelength of 0.000768 meters. write this number in scientific notation.

Explanation:

Step1: Recall standard - notation rule for scientific notation

For a number in scientific notation $a\times10^{n}$, when $n>0$, we move the decimal point $n$ places to the right.
For $1.21\times 10^{5}$, we move the decimal point 5 places to the right.
$1.21\times10^{5}=121000$

Step2: Recall scientific - notation rule for decimal numbers

For a number $x$ between 0 and 1, we write it in scientific notation as $a\times 10^{-n}$, where $1\leqslant a<10$ and $n$ is the number of places we move the decimal point to the right to get a number between 1 and 10.
For $0.000768$, we move the decimal point 4 places to the right to get $a = 7.68$. So $0.000768=7.68\times 10^{-4}$

Answer:

(a) 121000
(b) $7.68\times 10^{-4}$