Answered

One Astronomical Unit (AU) is 1.496 × 108 km, chosen because it is the average
distance from the Sun to the Earth. The Earth is about 6.7 x 103 km in diameter.
How many AU is the diameter of Earth? Make sure your answer includes the
correct number of significant digits.
Pick the correct answer
O
O
0.2232 × 105 AU
1.0232 × 10-5 AU
4.5× 10-5 AU
10 × 1011 AU
1.0× 1012 AU



Answer :

sqdancefan

Answer:

  (c)  4.5×10⁻⁵ AU

Step-by-step explanation:

You want the 6.7×10³ km diameter of the Earth expressed in terms of astronomical units (AU), which are 1.496×10⁸ km.

Diameter

  [tex]\dfrac{6.7\times10^3\text{ km}}{1.496\times10^8\ \dfrac{\vphantom{\overline{B}}\text{km}}{\text{AU}}}}\approx\boxed{4.5\times10^{-5}\text{ AU}}[/tex]

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Additional comment

The diameter is expressed using 2 significant figures, which is fewer than the number expressing the length of an AU. Hence the answer needs to be rounded to 2 significant figures.

As with all units conversion problems, you can think of the conversion factor as an "identity element." Its value is 1, because its numerator (1.496×10⁸ km) is equal to its denominator (1 AU). Multiplying or dividing by such a factor does not change the value. It only changes the units.

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