Understanding What

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Understanding What
Numbers Tell Us
Mr. K. NASA/GRC/LTP Edited Ruth Petersen
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• Preliminary Activities
• Be prepared to do some in-class arithmetic! You
  are required to know
• the speed of light in km/s
• the earths circumference
• the distance from the earth to the moon, the
  sun, Pluto, and the next closest star.
• how to represent a number in scientific notation
  (e.g., 1,000 103 ).

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Purpose It is important to think carefully about
situations and ideas that you encounter in life.
This activity is designed to provide practice in
thinking carefully.
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Imagine that you are an explorer in Wonderland,
and you have just found a number artifact. . .
??????
,000
1,000,000,000
1
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What do you make of this? If you were Indiana
Jones, what types of questions would you ask at
this point?
Does it have a name?
How big is it?
Why is it significant?
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The artifact is the number one trillion -
Imagine that you are an explorer in Wonderland,
and you have just found a number artifact. . .
Right !!!!!!
,000
As for the rest
1,000,000,000
1
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First, lets consider How big is it? How would
you approach this question?
,000
1,000,000,000
1
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To begin Can we make a comparison with how many
seconds there are in a day? A year?
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?
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Lets do some arithmetic!
Seconds in a Day
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s/m X
m/hr X
hr/day
60
60
86,400 s/day

Seconds in a Year!!! 86,400 s/day X 365.25
day/yr 31,557,600 s/yr
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Are these numbers even close to 1,000,000,000,000?
What percentage of 1,000,000,000,000 is 31, 557,
600?
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How about making a comparison with how many
seconds weve been alive?
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Mr. K. is 50 years old.
50 yr X
31,557,600 s/yr
1,577,880,000 sec

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Well, when I say that Im working on my second
billion, I now know what I really mean!
What percentage of 1,000,000,000,000 is 1, 577,
880, 000?
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How well are we doing so far?
.
OK, Lets come at it another way If I told you
that I was a trillion seconds old, what would be
my age in years?
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My age would be
What do you conclude from all this? Does this
help you to understand how big a trillion is?
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Next, lets consider Why is this number artifact
significant?
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Well, the U.S. National debt is 6 Trillion!
At 1 per second, how long would it take to
count? (Take a minute to work it out! )
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6
X
31,558 years

189,348 years!
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And not only that, the number of kms in a light
year are
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Wait! From your knowledge of the speed of light,
can you determine how many kms there are in a
light year?
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(Hint A light year is the distance that light
travels in one year.)
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In your pre-conference activities, you should
have found that c 300,000 km/s You also
probably know that distance S is speed X time S
c X t
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SoHow far does light travel in 1 second? 1
minute? 1 hour? 1 day? 1 year? (Show results in
scientific notation where appropriate. )
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What can you say about the last number on the
last page???
Answer In 1 second s 300,000 km In 1
minute s 18,000,000 km In 1 hour s
1,080,000,000 km In 1 day s 2.6 X 1010 km In 1
year s 9.5 X 1012 km
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• Now, compare these distances to the distances you
  already found in your pre-conference activities
• The Earths circumference
• The distance to the moon
• The distance to the sun
• The distance to Pluto
• The distance to the next nearest star
• State these distances in appropriate light units
  (light-second, light-minute, and so on). You have
  five minutes to do this work in class.

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The earths circumference is 0.125 light
seconds. The moon is 1.3 light seconds away. The
sun is 8.3 light minutes away. Pluto is over 5
light hours away. The nearest star is 4.3 light
years away!
Factoid!!! With NASAs Hubble Telescope, we can
see out to about 10 billion light years!!
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What does this tell you about the cosmos? Did you
ever think about the cosmos the way you are
thinking about it right now?
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Follow-up Activity With NASAs Hubble Telescope,
we can see out to about 10 billion light years.
We now estimate (very roughly) that there may be
on the order of 5 sextillion stars in the
observable universe. So
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1. Look up sextillion in your dictionary,
express it in scientific notation, then compare
it to other large numbers that you might have
learned in school such as Avogadros number. 2.
Are there more (1) stars in the observable
universe or (2) molecules in a mole of water? 3.
How many cubic centimeters IS a mole of water?
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joseph.c.kolecki_at_grc.nasa.gov