Transcript http://biophysics.asu.edu/outreach/presentations/LargeNumbers.ppt

Large numbers
Orders of magnitude and
proportional reasoning
Length scale by a power of ten
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One D

Ten Ds

Fifty Ds
D
DDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

How can you represent the length of 100
D’s and make it fit on the screen?
Very large and small distances

How do we represent large and small
distances relative to each other?


We use models to visualize what we can’t see
with the naked eye.
Representations of atoms, molecules, and
planets are a few examples of using this
idea.
What can you see?
Is it possible to see an inch and a mile at
the same time?
 How about 1 inch and 10 miles?
 How about 1 inch and 100 miles?


We use scaling to represent large
distances so we can make sense of how
far a large distance really is.
How far is it…?
To Taco Bell?
About .5 miles
To Tucson?
About 100 miles
Relative size
Maps use the idea of scaling
 If one inch represents one mile, how many
inches would you need from Mesa, AZ to
Tucson, AZ?
 What are the units for this scale?

Is this a reasonable size for a useful
model?
 What might be a better representation?

How far is it…?
To the moon?
220,000 miles
To the sun?
93 million miles
Scaling using a proportion

If we want to use a dry erase marker to
represent the distance from the earth to
the moon, what would the scale of the
marker be? Remember to include the
units!!!
Scaling using a proportion

How many markers would be needed to
represent the distance from the earth to
the sun?

How many markers to represent a light
year (about 5,850,000,000,000 miles)?
Planet size
If the Earth (d=7,900 miles was
represented using a tennis ball (d=2.5
inches), how big would a ball that
represents the Jupiter (d=89,000 miles)
have to be?
 Discuss the technique your group used to
solve the problem.


Do we know of a ball this size that we
could use for this model?
The Sun
How big would the ball that represents the
sun (d=870,000 miles) have to be with the
tennis ball representing earth again?
 What ball would you use to represent the
sun?
 Can you design a better model to compare
the earth and the sun?

Your assignment

Develop a model for all of the planets in
our solar system. Include the Earth’s
moon and the Sun, but don’t include Pluto.
Make sure the representation you create is
to the actual scale. See the handout for
actual size of the planets.