Question

answer the following. (a) an astronomers infrared telescope is able to detect radiation with a wavelength of 9.57 * 10^(-4) meters. write this number in standard notation. (b) the diameter of jupiter at its equator is approximately 143,000 kilometers. write this number in scientific notation. (a) meters (b) kilometers

Explanation:

Step1: Convert to standard notation

For a number in scientific - notation \(a\times10^{-n}\) (\(n>0\)), move the decimal point \(n\) places to the left. Given \(9.57\times 10^{-4}\), move the decimal point 4 places to the left. So \(9.57\times 10^{-4}=0.000957\).

Step2: Convert to scientific notation

For a number \(N\), scientific notation is of the form \(a\times 10^{n}\), where \(1\leqslant|a|<10\) and \(n\) is an integer. For \(143000\), move the decimal point 5 places to the left to get \(a = 1.43\) and \(n = 5\). So \(143000=1.43\times 10^{5}\).

Answer:

(a) \(0.000957\)
(b) \(1.43\times 10^{5}\)