understanding what mr. k. nasa/grc/ltp edited: ruth petersen numbers tell us

Understanding What

Mr. K. NASA/GRC/LTPEdited: Ruth Petersen

Numbers Tell Us

Preliminary Activities:

Be prepared to do some in-class arithmetic! You are required to know:

1. the speed of light in km/s

2. the earth’s circumference

3. the distance from the earth to the moon, the sun, Pluto, and the next closest star.

4.how to represent a number in scientific notation (e.g., 1,000 = 103 ).

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.

Imagine that you are an explorer in Wonderland, and you have just found

a number artifact. . .

1,000,000,000,000????

??

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?”

Imagine that you are an explorer in Wonderland, and you have just found

a number artifact. . .

1,000,000,000,000

The

artifact is

the

number

one

trillion -

Right !!!!

!! As for

the

rest…

First, let’s consider: “How big is it?”

How would you approach this question?

1,000,000,000,000

To begin: Can we make a comparison with how many seconds there are in a

day? A year?

?

?

Let’s do some arithmetic!

24

86,400 s/day

s/m X m/hr X hr/day60 60

=

Seconds in a Day…

Seconds in a Year!!!

86,400 s/day X 365.25 day/yr

= 31,557,600 s/yr

Are these numbers even close to 1,000,000,000,000?

What percentage of 1,000,000,000,000 is 31, 557, 600?

31,557, 6001,000,000,000,000

X 100% = 0.003%

.

How about making a comparison with how many seconds we’ve been alive?

Mr. K. is 50 years old.

50 yr X

1,577,880,000 sec=

31,557,600 s/yr

What percentage of 1,000,000,000,000 is 1, 577, 880, 000?

1,577,880,0001,000,000,000,000

X 100% = 0.158%

Well, when I say that I’m working on my second billion, I now know what I

really mean!

.

OK, Let’s come at it another way:

If I told you that I was a trillion seconds

old, what would be my age in years?

How well are we doing so far?

What do you conclude from all this? Does this help you to understand how

big a trillion is?

1,000,000,000,000 sec 31,557,600 s/yr

31,688 years??

=

My age would be…

.

Next, let’s 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! )

6 X31,558 years=189,348 years!

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And not only that, the number of kms in a light year are…

Wait!

From your knowledge of the speed of light, can you determine how many

kms there are in a light year?

(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

So…How far does light travel in:

1 second?

1 minute?

1 hour?

1 day?

1 year?

(Show results in scientific notation where appropriate. )

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

What can you say about the last number on the last page???

Now, compare these distances to the distances you already found in your pre-conference activities:

•The Earth’s 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.

The earth’s 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 NASA’s Hubble Telescope, we can see out to about 10 billion light

years!!

What does this tell you about the cosmos? Did you ever think about the

cosmos the way you are thinking about it right now?

Follow-up Activity:

With NASA’s 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…

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 Avogadro’s 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?

joseph.c.kolecki@grc.nasa.gov