Part a: the sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds? part b: which is the more reasonable measurement of the diameter of a human hair: 1.8 ⋅ 10−2 mm or 1.8 ⋅ 102 mm? justify your answer.

A) To multiply numbers in scientific notation we first multiply the coefficients, round to the number with less significant figures in the coefficients, and then add the exponents of the ten bases: 3.9*1.55 = 6.0 and 33+7 = 40, so the sun produces 6.0 ⋅ 1040 ergs of radiant energy in 1.55 ⋅ 107 seconds.

B) The diameter of a human hair is far tinier than a 1 mm so we can rule out 1.8 ⋅ 102 mm since is a bigger unit; therefore the answer is 1.8 ⋅ 10−2 mm.