Question

answer the following. (a) an astronomers infrared telescope is able to detect radiation with a wavelength of 3.81×10^(-5) meters. write this number in standard notation. (b) the diameter of mercury at its equator is approximately 4880 kilometers. write this number in scientific notation.

Explanation:

Step1: Convert scientific to standard

For a number in scientific - notation $a\times10^{-n}$ ($n>0$), move the decimal point $n$ places to the left. Given $3.81\times 10^{-5}$, move the decimal point 5 places to the left.
$3.81\times 10^{-5}=0.0000381$

Step2: Convert standard to scientific

For a number $N$, to write it in scientific - notation $a\times 10^{n}$, where $1\leqslant|a|<10$ and $n$ is an integer. For $4880$, move the decimal point 3 places to the left to get $a = 4.88$ and $n = 3$. So $4880=4.88\times 10^{3}$.

Answer:

(a) $0.0000381$
(b) $4.88\times 10^{3}$