Question

answer the following.
(a) an astronomer’s infrared telescope is able to detect radiation with a wavelength of $5.32 \times 10^{-4}$ 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.
(a) \\(\square\\) meters
(b) \\(\square\\) kilometers

Explanation:

Part (a)

Step1: Recall standard notation for negative exponents

To convert \(5.32\times10^{-4}\) to standard notation, we move the decimal point 4 places to the left (because the exponent is -4).
\(5.32\times10^{-4}=0.000532\)

Part (b)

Step1: Recall scientific notation format

Scientific notation is in the form \(a\times10^{n}\) where \(1\leqslant|a|\lt10\) and \(n\) is an integer. For 121000, we move the decimal point 5 places to the left to get \(a = 1.21\) and \(n=5\).
\(121000 = 1.21\times10^{5}\)

Answer:

(a) \(0.000532\) meters
(b) \(1.21\times10^{5}\) kilometers