Saturday, September 1, 2012

Large Number Names for Those Who Wish to Understand My Blogs on the Universe

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This article shows all the large number names as well as how to write and understand scientific notation, which is used constantly in astronomy due to massive numbers.
Names for large numbers
English name
104Ten Thousand10,000
105Hundred Thousand100,000
(There are many more numbers, but they simply follow the number-prefix (quad 4, quin 5, sex 6, etc) pattern seen above, but not many things are described by anything beyond a quattuordecillion. I've seen only a handful of instances).

Other large numbers (color coded for ease of reading)
10100 - Googol - 1 followed by 100 zeroes

10303 - Centillion - 1 followed by 303 zeroes


10Googol - Googolplex - 10(10100) could not write these zeroes on a quadrillion books in size 8 font, literally
10Googolplex- Googolplexplex - (1010^10^100) impossble to fit the zeroes in entire universe, literally
Which looks like this still in its exponent form: 1010100 =


Why bother to understand to numbers? Well, there are some good reasons below. Check out the definition below and why it just seems so empty, followed by some good illustrations of how the word "Universe" would really feel like to a space traveler.
  1. UNIVERSE--all matter and energy in space: the totality of all matter and energy that exists in the vastness of space, whether known to human beings or not
What does that definition mean to you? It has so little feeling to it, although it sounds fairly all-encompassing. What is a lot? What is even more? What is "totality?" Words like totality tend to stand alone, as they aren't used much and don't have many commonly used synonyms that the average person uses on a regular basis. You will find synonyms in your head like gigantic, colossal, gargantuan, or maybe simpler words such as everything, vastness is another good one, or endlessness even. Yet none of those illustrate the size or power of this magnitude. What is the word endless to a person who cannot live long enough to see the word in its reality? People think their 8 hour shifts at work are endless. A building can be gigantic when a person looks straight up at one, and a whale is a gargantuan sea creature weighing well over 20,000 lbs. and capable of swallowing several humans whole at the same time! A skyscraper may seem colossal when it stands higher than the mountains of Earth, but with these illustrations in mind, how inadequate are these words when they are used to describe "all existence?" When something is truly endless, perhaps it is better to illustrate the "feeling" behind the word with numbers that trigger your imagination.
Big numbers are a pain to write, astronomers use Scientific Notation constantly. It is truly easy, and contrary to my blogs, I am surprisingly bad with math. My blog contains basic math, even though the numbers are massive.
Just what the hell is 1×106 ? It's very simple, just think of 1 + 6 zeroes, so that's 1,000,000.
--See the "6" exponent? Write down that many zeroes
000 000
See the "1" on the left? Write a 1 to the left of the zeroes
1 000 000
Voila. You solved it! One Million! And yes, scientific notation is always this easy to do. If you plug the notation into a calculator it will simply come up as 1,000,000 too.
Take 1.22×106 and follow the below instructions:
1) Write down all the numbers to the left of the decimal
2) 106 means 6 zeroes, so write down the six zeroes
1 000 000
3) Almost done now! On the 1.22 the ".22" counts as two zeroes, so write the 22 over top of the leftmost two zeroes, which leaves four zeroes behind the it:
1 220 000
4) Now add commas starting with the rightmost numbers
1,220,000 = 1.22×106
Eventually you'll memorize what the exponents mean and no actual solving will be required. For instance, when you see 1061 you will eventually just think 1,000,000, and anything × it is simply "" times one million.
SOLVE 10.987654×1012 using the same procedures above. Don't let the numbers confuse you:
1) Write down all the numbers to the left of the decimal
2) 1012 means 12 zero digits, so write down the 12 zeroes
10 000 000 000 000
3) Write the 987 654 over top of the leftmost zeroes
10 987 654 000 000
4) Now add commas starting with the rightmost numbers
10,987,654,000,000 = 10.987654×1013
5) Now double check your numbers by counting the 13 numbers after the 1 (the leftmost digit does not count as a zero, so there should be 13 digits. 12 of which are considered zeroes counted in the exponent.
**Keep in mind***
1×106 is 1 000 000
10×105 is 1 000 000
1000×103 is 1 000 000
10 000×102 is 1 000 000
100 000×101 is 1 000 000
Basically, the leftmost number can take away from the exponent by taking zeroes from the right and putting them on the left, but what is the point? It makes more sense to shorten the number to single digits. The 1×106 makes more sense to write than the 10×10003 !! It's shorter and more concise. In fact, the whole reason scientific notation exists is simply to shorten numbers as much as possible.
For numbers less than 1 (decimals) such as 0.1, the steps above are still followed, but can seem different, but it's really all the same. Don't be intimidated.
(Some of this is in reverse, so don't let yourself be intimidated!)
Take 5.1×10-4 and follow the below instructions:
1) Write down all the numbers to the left of the decimal
2) 10-4 means 4 zeroes, so write down the four zeroes
0000 5
3) Almost done now! On the 5.1 the "5" counts as a zero, so write the 51 over top of the rightmost zero, which leaves three zeroes in front of it:
4) Now add the decimal point to the far left
Voila! See that was easy.
Other equations will have a decimal×whole number like below, these you have to actually multiply until you become more familiar with rearranging the digits:
0.0005×102 is "five ten-thousandths"
102 =100 so
=0.05 "five one-hundredths." The ×100 forced the 5 over by one one-hundredth
The 102 simply causes the decimal to become bigger, forcing the "5" over toward the left. When a decimal gets BIGGER it moves closer to the decimal point off to the left until it passes it, becoming a whole number. So 0.05 is 100× larger than 0.0005
Count in your head all the digits representing each number:
0.0005= 0 tens, 0 hundreds, 0 thousands, 5 ten thousands
and ×100 means the 5 will move to the left two decimal places, where ×1000 would move the 5 three spaces, and ×10,000 would cause the 5 to become a whole number, 5.0. Since it is five ten-thousandths, it would need to be multiplied by 10,000 to become a whole number.
0.5 needs ×10 to become a 5
0.05 needs ×100 to become a 5
0.005 needs ×1,000 to become a 5
0.0005 needs ×10,000 to become a 5
0.00005 needs ×100,000 to become a 5
And so on and so on. You'll get it eventually. It's muscle memory, not smarts.
Other equations may also seem confusing because they may contain a huge numbers multiplied by a decimal and still come up as a whole number. These actually work as percentiles, where:
1,000,000,000×0.05 is simply 5% of One Billion, = 50,000,000 (fifty million)
0.0000000015468×1021 is massive enough that it will go from a tiny number to a massive whole number
1021 = 1,000,000,000,000,000,000,000
= 1,546,800,000,000 (1.5468 trillion)
Now you're a mathematician! Congrats!

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