Saturday, April 21, 2007

How High Can You Count?

http://isthe.com/chongo/tech/math/number/howhigh.html

It's a very interesting article about the English number system and it teaches you how to say 10^10000000000 and larger numbers.

I will give a summary of that article here...

Here's the sequence (not complete): million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion (10^33), undecillion, dodecillion,..., vigintillion (10^63),..., trigintillion (10^93),..., centillion(10^303), cenuntillion(10^306),..., ducentillion(10^603),..., milliatillion(10^3003),..., and to infinity.

prefixes for 1~10:
un, do, tre, quattuor, quin, sex, septen, octo, novem

prefixes for 10, 20,...., 90:
dec, vigin, trigin, quadragin, quinquagin, sexagin, septuagin, octagin, nonagin

prefixes for 100, 200, 300,..., 900:
cen, ducen, trecen, quatringen, quingen, sescen, septingen, octingin, nongin

prefix for 1000: millia

So, let's say you want to know how to say 2 * 10^654

1. because the number system goes by every 3 digits, we divide 654 by 3

654 / 3 = 218

2. then, we subtract one from it because "thousand" goes before the million, billion...etc

218 - 1 = 217

3. we say that using the prefixes by the order: hundreds -> ones -> tens and the thousands act as in normal English

217 = 200 + 7 + 10 = ducen-octo-decillion = ducenoctodecillion

4. we got it!
2 * 10 ^ 654 = two ducenoctodecillion!


Wanna try a harder one?

987654 000,...., 000 (1756 sets of 000's)

We break that down to each set

987654 000,...., 000 = 987 * 1000^1757 + 654 * 1000^1756

Then, we subtract one from the power and convert that into words

1757 = millia-septingen-septen-quinquagin-tillion

1756 = millia-septingen-sexa-quinquagin-tillion

We are done!

987654 000,...., 000 = nine hundred eighty-seven milliaseptingenseptenquinquagintillion six hundred fifty-four milliaseptingensexaquinquagintillion

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