Converting Units
Two different ways to convert units will be described below. In each case, you need a
conversion equation. That may be as simple as 1 day = 24 hours, or 1 inch = 2.54 cm.
Let’s try converting 4.5 miles into feet:
Method 1
Method 2
The conversion equation is:
1 mile = 5280 feet.
The conversion equation is:
1 mile = 5280 feet.
Set up ratios, matching the units:
4.5 miles
1 mile
=
OK
x feet
5280 feet
Multiply our number by a fraction
x feet
5280 feet
=
4.5 miles
1 mile
4.5 miles !
The fraction will be made up of the 2
sides of our conversion equation. Which
part should go on the bottom? We need
to get rid of the miles, so they go on the
bottom.
OK
4.5 miles 5280 feet
=
NOT OK
x feet
1 mile
4.5 miles !
Let’s take the 1st set of ratios, and crossmultiply:
1 mile
Finishing the fraction:
4.5 miles ! 5280 feet = x feet ! 1 mile
4.5 miles !
Solving for x yields
x = 23760 feet.
Convert 100 days into years:
6
5280 feet
= 23760 feet
1 mile
Scale Factors
Astronomy relies heavily on pictures and images. Scale factors allow us to measure one
thing in comparison to another thing that is known.
A
B
In this picture, assume ball A is 3.4 mm across. Ball
B is also 3.4 mm across. If ball B is really 30 cm
across, what is the diameter of ball A?
C
In this picture, assume point C is 2 times as far from
the X as is point D. If point D is really 7.2 meters
from the X, how far away from the X is point C in
reality?
D
E
F
In this picture, assume rectangle E is 17 cm long and
rectangle F is 11 cm long. If rectangle F is really
3.0 m long, how long is rectangle E?
x
Assume line G is 5 cm from line x in the picture, and
line H is 8 cm from line x. In reality, line H is
9 nm from line x. How far is line G from line
x in reality?
Write a description (in your own words) for doing a scale factor:
7
G
H
Distance = Rate x Time
or:
distance = speed x time
or:
distance = velocity x time
{velocity is the speed with a direction}
If you know two of the three things involved, you can find the third. Suppose we know
the speed and the time traveled. Then we just use the equation to find the distance.
Example:
If we drive at 88 km / hr and traveled for 2.5 hours, how far did we go?
Suppose we know the speed and distance. How do we find the travel time?
Start with our equation:
distance = speed x time
To isolate the time on one side, we need
to get rid of the speed. How do we do
that? Write out your equation:
What if we know the distance and time?
Solve for the speed:
distance = speed x time
If you traveled 25,000 km at 4 km / hr, how long did you travel?
If you traveled 14 km and it took 45 minutes, how fast did you travel (in km / hour)?
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Math and Measurements
Scientific Notation
Rewrite the following:
10,000 =
100,000,000 =
0.001 =
-0.00004 =
900 =
0.023 =
410,680 =
5 ! 10 3 =
8.3 ! 10 "4 =
! 2.601 " 10 5 =
8.09 ! 10 "1 =
123
. ! 10 9 =
Solve the following:
( 6 ! 10 "3 ) ÷ ( 2 ! 10 "2 ) =
(3 ! 10 6 ) ! ( 4 ! 10 "1 ) =
( 6 ! 10 9 ) / ( 2 ! 10 4 ) =
3000 ! (5 ! 10 5 ) =
( 6 ! 10 3 ) + ( 4 ! 10 2 ) =
(35
. ! 10 4 ) + 1053 =
(3 ! 10 2 ) " (1 ! 10 5 ) =
123456789 + ( 7 ! 1011 ) =
Units
Do the following conversions of metric units:
7 km = __________ m
8 kg = __________ g
6.35 kg = __________ g
4.32 g = __________ mg
8.25 km = __________ cm
0.97 cm = __________ mm
70 cm = __________ mm
0.825 km = __________ cm
If you want 2 pounds of sausage in Germany, how many kilograms do you need to ask
for?
If you run 5 miles, how many kilometers have you run? How many meters?
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How many seconds are in one year?
Distance = Rate x Time
If you traveled for 3 hours at 7 m/sec, how many kilometers did you travel?
The Space Shuttle orbits the Earth in about 90 minutes. About how fast does it travel?
How many kilometers away is the star Sirius? If you traveled at the normal speed of a
car, how many years would it take for you to get there?
10
Measurements
In the Hubble Space Telescope picture below, measure the “scale” diameter of Pluto and
its moon, Charon (in mm). Then measure their "scale" distance apart.
Given that the real diameter of Pluto is 2300 km, find the real diameter of Charon, and its
distance from Pluto.
Pluto
Charon
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Given that the diameter of Saturn is 120,540 km, find the diameter of the rings.
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