Sunday, January 5, 2020

Understanding Very Large Numbers

Have you ever wondered what number comes after a trillion? Or how many zeros there are in a vigintillion? ​Some day you might need to know this for a science or math class, or if you happen to enter one of several mathematical or scientific fields.   Numbers Bigger Than a Trillion The digit zero plays an important role as you  count very large numbers. It helps to  track these multiples of 10  because the larger the number is, the more zeros are needed. Name Number of Zeros Groups of 3 Zeros Ten 1 0 Hundred 2 0 Thousand 3 1 (1,000) Ten thousand 4 1 (10,000) Hundred thousand 5 1 (100,000) Million 6 2 (1,000,000) Billion 9 3(1,000,000,000) Trillion 12 4 (1,000,000,000,000) Quadrillion 15 5 Quintillion 18 6 Sextillion 21 7 Septillion 24 8 Octillion 27 9 Nonillion 30 10 Decillion 33 11 Undecillion 36 12 Duodecillion 39 13 Tredecillion 42 14 Quattuordecillion 45 15 Quindecillion 48 16 Sexdecillion 51 17 Septen-decillion 54 18 Octodecillion 57 19 Novemdecillion 60 20 Vigintillion 63 21 Centillion 303 101 Grouping Zeros by Threes Many  people  find it easy to understand that the number 10 has one zero, 100 has two zeros, and 1,000 has three zeros. These numbers are used all the time in daily living, whether it is dealing with money or counting something as simple as our music playlist or the mileage on our cars. When you get to million, billion, and trillion, things become a little more complicated. How many zeros come after the one in a trillion? Its hard to keep track of that and count each individual zero, so  these long numbers  have been broken down into groups of three zeros. For example, its much easier to remember that a trillion is written with four sets of three zeros than it is to count out 12 separate zeros. While you might think that ones pretty simple, just wait until you have to count 27 zeros for an octillion or 303 zeros for a centillion. Then you will be thankful that you only have to remember nine and 101 sets of three zeros, respectively. Powers of 10 Shortcut In mathematics  and science, you  can rely on the powers of 10 to quickly express exactly how many zeros are needed for these larger numbers. For example, a shortcut for writing out a trillion is 1012  (10 to the power of 12). The 12 indicates that the number  needs a total of 12 zeros. You can see how much easier these are to read than if there were just a bunch of zeros: Quintillion 1018 or 1,000,000,000,000,000,000 Decillion 1033  or 1,000,000,000,000,000,000,000,000,000,000,000 The Enormous Numbers: Googol and Googolplex You are probably very familiar with the search engine and tech company Google. Did you know that the name was inspired by another very large number? Though the spelling is different, the  googol  and the  googolplex  played a role in the naming of the tech giant. A googol has 100 zeros and is expressed as 10100. It is often used to express any large quantity, even though it is a quantifiable number. It makes sense that the largest search engine that pulls a large quantity of data from the internet would find this word useful. The term googol was coined by the American mathematician Edward Kasner in his 1940 book, Mathematics and the Imagination. The story goes that Kasner asked his then 9-year-old nephew, Milton Sirotta, what to name this ridiculously long number. Sirotta came up with  googol. But why is a googol important if its actually less than a centillion? Quite simply, a  googol is used to define a  googolplex.  A googolplex is 10 to the power of googol, a number that boggles the mind. In fact, a googolplex is so large that theres really no known use for it. Some say that it even exceeds the total number of atoms in the universe. The googolplex is not even the largest number defined to date. Mathematicians  and scientists have also devised Grahams number and Skewes number. Both of these require a math degree to even begin to understand. Short and Long Scales of a Billion If you thought the concept of a googolplex is tricky, some people cannot even agree on what defines a billion. In the U.S. and most of the world, it is accepted that 1 billion equals 1,000 million. It  is written as 1,000,000,000 or 109. This number is used often in science and finance, and it is called the short scale. In the long scale, 1 billion is equal to 1 million million. For this number, you will need a 1 followed by 12 zeros: 1,000,000,000,000 or 1012. The long scale was first described by Genevieve Guitel in 1975. It is used in France and, for a time, was accepted in the United Kingdom as well.

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