 We've discussed big numbers, and how long it would take to count to them. On this page we'll look at the biggest numbers of all! A Googol A googol is the large number 10100 This is: 10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x 10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x 10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x 10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x 10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10x10 or the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 The term 'googol' was invented in 1920 by 9-year-old Milton Sirotta, the nephew of mathematician Edward Kasner. He may have been inspired by the contemporary comic strip character Barney Google. Kasner then popularized the concept in his 1940 book 'Mathematics and the Imagination'. A googol has no special significance in mathematics. It is useful, however, when comparing very large quantities, such as the number of subatomic particles in the visible universe (1080), or the number of possible chess games (10120). To give a sense of how big a googol really is, consider the mass of an electron, at just under 10-30 kg. Compare this to the mass of the visible universe, estimated at between 1050 and 1060 kg. The universe's mass is about 1080 to 1090 times bigger than the mass of an electron. This number is at most one ten-billionth of a googol. Carl Sagan pointed out that the total number of elementary particles in the universe is around 1080 and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be 10128 of them. If the observable universe of today were filled with sand, it would still only equal 1095 grains. Another 100,000 observable universes filled with sand would be necessary to make a googol. The heat death of the expanding universe will be at least one googol years in the future. A googol is approximately 70! This is factorial notation from Math 30; 70x69x68x67x66x ... x3x2x1. A Googolplex A googolplex is the number 10googol, or equivalently, 1010100. Written out in ordinary decimal notation, this is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeros. Needless to say, we aren't going to attempt to write that out. A typical book can be printed with 106 (one million) zeros ... this is 400 pages with 50 lines per page and 50 zeros per line. Therefore, it requires 1094 such books to print all the zeros of a googolplex (that is, printing a googol of zeros). If each book had a mass of 100 grams, all of them would have a total mass of 1093 kilograms. In comparison, Earth's mass is 5.972 × 1024 kilograms, the mass of the Milky Way galaxy is estimated at 2.5 × 1042 kilograms, and the total mass of all the stars in the observable universe is estimated at To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the masses of the Milky Way and the Andromeda galaxies combined (by a factor of roughly 2.0 × 1050), and greater than the mass of the observable universe by a factor of roughly 7 × 1039 In the PBS science program 'Cosmos: A Personal Voyage', Episode 9: "The Lives of the Stars", astronomer and television personality Carl Sagan estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of the observable universe is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different combinations in which the particles could be arranged and numbered would be about one googolplex. Additional Notes: We've been using Scientific Notation. Review how it works here. The names for big numbers you're familiar with, since about grade 6 math, are: Ones (100), Tens (101), Hundreds (102), Thousands (103), Ten thousands (104), Hundred thousands (105), Millions (106), Ten millions (107), Hundred millions (108), Billions (109), Ten billions (1010), Hundred billions (1011), Trillions (1012), Ten trillions (1013), Hundred trillions (1014) But there are more groups ... Quadrillions (1015), Quintillions (1018), Sextillions (1021), Septillions (1024), Octillions (1027), Nonillions (1030), Decillions (1033), ... Eddington number (1080), ... Googol (10100), ... Shannon number (10120), ... Googolplex (1010100) The Eddington number, named for British astrophysicist Arthur Eddington, is the total number of protons in the universe: 1080 The Shannon number, named after the American mathematician Claude Shannon, is the number of possible chess games: 10120 For even larger numbers that are rarely discussed, see our page on tetration! |