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Astro 10: Math Review
Problem 1: Scientific Notation
Astronomy uses very large and very small numbers. Astronomers are also sort of lazy. As a result, we use
scientific notation so we don’t have to spend so much time writing out zeros. Make the following numbers look
more science-y by writing them in scientific notation.
a) 1,010,000
b) .0004673
c) 124,540
d) .000000615
e) 31,500,000
Problem 2: Exponents
Solve the following problems. Express your answer in exponential form. They look cooler that way.
a)103 × 109 =
b) 711 × 723 =
c) (54 )2 =
d) 27 × 43 =
e) 67 /63 =
f) 125 × 12−13 =
g) a−3 /a−8 =
h) (8a3 )/(2a)3 =
i) (105 )1/3 =
Problem 3: Converting Units
a) How many seconds are there in a year? Don’t worry about plugging in numbers to get an answer for this. It
is far more important that you set it up correctly. Can you think of a reason why seconds is not a very useful
way to tell someone your age?
b) A light-year is unit of length defined to be the distance light travels in one year. If light travels 3×105 km/s,
how many kilometers are there in one light-year? A useful equation to remember is distance = velocity × time.
If you didn’t plug in for the previous problem and find yourself needing that result, then use the number from
1(e).
c) The Sun’s nearest neighboring star is Proxima Centauri which is 4 × 1013 km away. How many years
would it take light to travel from Proxima Centauri to the Sun. An equivalent way of asking this question is
how many light years away is Proxima Centauri? How many miles away is this? (There are approximately 1600
meters in 1 mile.)
Problem 4: Ratios
Ratios will be your best friend in this class. Use ratios to solve the following problems. Round your answer to
only one decimal place.
a) Let’s scale the Sun, which has a radius of 7 × 105 km, down to the size of a basketball which has a radius of 10 cm. If the actual distance from the Sun to the Earth is 1.5 × 108 km, how far away would the Earth
be in our scaled down version of the solar system? Would you be able to fit the Earth and the Sun in your
living room?
b) How far away would Proxima Centauri be in our scaled down universe? Now convert your answer to units of
football fields recalling that there are 100 yards in a football field and 1.1 yards in a meters. What does this say
about distances between stars in space? Would Cal running back (and potential Heisman Trophy candidate!)
Marshawn Lynch be able to run this distance for a touchdown?
c) You are making your favorite pizza. After tossing the dough up for a few minutes and trying out your best
Italian accent, you flatten the dough on a table making a perfect circle of radius 6 in. You place your pizza in
the oven and bake. Upon taking your pizza out you find your pizza is still a perfect circle but now has a radius
of 12 in. By how much has the area of the pizza increased? (Recall that the area of a circle is given by A = πr2 ,
though you will not need to know the value of π to solve this problem)
d) It takes about 8 minutes for light to ravel from the Sun to the Earth. How long would it take an airplane
traveling the speed of sound ( 340 m/s) to make the same trip (you don’t need to know the distance to the
sun!)?