Question

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 3.25 ⋅ 103 seconds? Express your answer in scientific notation and show your work. (5 points)

Part B: Which is the more reasonable measurement of the distance between the tracks on a railroad:
1.435 ⋅ 10−3 mm or 1.435 ⋅ 103 mm? Justify your answer. (5 points)

Answer 1

5914 1404 393

Answer:

A) 1.3×10^37 ergs

B) 1.435×10^3 mm

Explanation:

A) The amount of energy will be the product of the energy rate and time:

(3.9×10^33 ergs/s)×(3.25×10^3 s) =12.675×10^(33+3) ergs

= 1.2675×10^(1+36) ergs

= 1.2675×10^37 ergs ≈ 1.3×10^37 ergs

The mantissa of the result is the product 3.9×3.25, adjusted to have one digit left of the decimal point. The exponent of the result is the sum of the exponents of the factors, adjusted by 1 to match the adjustment in the mantissa.

The final value should be rounded to 2 significant figures, reflecting the precision of the sun's energy production.

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B) A millimeter is a small fraction of an inch. 10^-3 mm is a small fraction of the width of a human hair, so 1.435×10^-3 mm is not a reasonable estimate of the distance between railroad tracks.

On the other hand, 1.435×10^3 mm is 1.435 m, almost 56.5 inches. This is a much more reasonable measurement of the distance between railroad rails.

1.435×10^3 mm is more reasonable