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## About how many times larger is the diameter of the Milky Way Galaxy than the diameter of Saturn’s rings? (Data: Saturn’s rings are about 270,000 km in diameter;

About how many times larger is the diameter of the Milky Way Galaxy than the diameter of Saturn’s rings? (Data: Saturn’s rings are about 270,000 km in diameter; the Milky Way is 100,000 light-years in diameter.)

Josh,
This is an example of unit conversion problem, whereby you alternate the units of numerators and denominators to convert from one unit of measurement to another.  This is more easily done when you convert the values into scientific notation.

The S.I. measurement for a lightyear is 9.461×1015m.

Now, using the numerator-denominator method of conversion and scientific notation:
1.0x105ly × 9.461×1015m ×    1km      = 9.461x1017km
1ly                 1.0x103m

Dividing:
9.461x1017km = 3.5x1012 times larger
2.7x105km

Note that with scientific notation, the number of significant figures is the least amount of significant figures of all given values, with in this case, because of 2.7x105, is 2.  Thus the answer is rounded to 3.5x1012.

Please let me know if you need me to clarify any of these concepts further.
Dear Josh,

(100,000 light years)*(9,454,254,955,500,000 meters/light year) =
(105 light years)*(9.454254955 x 1012 meters/light year) = 9.454254955 x 1017 meters
or 9.454254955 x 1014 kilometers

Ratio = Milky Way            = 9.454254955 x 1014 kilometers          = 3.50158 x 109
_________               __________________________
Saturn's Rings           2.7 x 105 kilometers
(9.4605284(10^15) m / light-year) (100,000 light-years) = 9.4605284(10^20) m

9.4605284(10^20) m / 270,000,000 m = (9.4605284/2.7)(10^12)

= 3,503,899,407,407