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Understanding What

Join Mr. K in this Math adventure as we delve into the vast realms of numbers, from seconds in a day to distances in light years, unveiling the significance of a trillion. Discover the wonders of the cosmos and ponder the vastness of the universe. Explore with NASA's Hubble Telescope and expand your understanding of the numerical universe.

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Understanding What

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  1. Understanding What Numbers Tell Us Mr. K. NASA/GRC/LTP Edited: Ruth Petersen

  2. Preliminary Activities: • Be prepared to do some in-class arithmetic! You are required to know: • the speed of light in km/s • the earth’s 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 ).

  3. 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.

  4. Imagine that you are an explorer in Wonderland, and you have just found a number artifact. . . ?????? ,000 1,000,000,000 1

  5. 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?”

  6. The artifact is the number one trillion - Imagine that you are an explorer in Wonderland, and you have just found a number artifact. . . Right !!!!!! As for the rest… ,000 1,000,000,000 1

  7. First, let’s consider: “How big is it?” How would youapproach this question? ,000 1,000,000,000 1

  8.  ? To begin: Can we make a comparison with how many seconds there are in a day? A year?  ?

  9. Let’s do some arithmetic! Seconds in a Day… 60 s/m X 60 m/hr X 24 hr/day 86,400 s/day = Seconds in a Year!!! 86,400 s/day X 365.25 day/yr = 31,557,600 s/yr

  10. 31,557, 600 X 100% = 0.003% 1,000,000,000,000 Are these numbers even close to 1,000,000,000,000? What percentage of 1,000,000,000,000 is 31, 557, 600?

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

  12. Mr. K. is 50 years old. 50 yr X 31,557,600 s/yr 1,577,880,000 sec =

  13. 1,577,880,000 X 100% = 0.158% 1,000,000,000,000 Well, when I say that I’m 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?

  14. How well are we doing so far? . • 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?

  15. 1,000,000,000,000 sec = 31,688 years?? 31,557,600 s/yr My age would be… What do you conclude from all this? Does this help you to understand how big a trillion is?

  16. . . . . . . . . . . . . Next, let’s consider: Why is this number artifact significant?

  17. 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! )

  18. 6 X 31,558 years = 189,348 years!

  19. . 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.) . . . . . .

  20. 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

  21. So…How far does light travel in: 1 second? 1 minute? 1 hour? 1 day? 1 year? (Show results in scientific notation where appropriate. )

  22. 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

  23. 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.

  24. 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!!

  25. What does this tell you about the cosmos? Did you ever think about the cosmos the way you are thinking about it right now?

  26. 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…

  27. 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?

  28. joseph.c.kolecki@grc.nasa.gov

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