You may have difficulties when you try to read large numbers in words. One and six zeros is a million, of course. But how do you call bigger numbers? For example, what comes after a trillion?
Table with numbers painted on the ground – illustrative photo. You do not meet numbers like a trillion in everyday life. Image credit: Markus Krisetya via Unsplash, free license
Is it True that Europeans and Americans Call Big Numbers Differently?
For Europeans, 1 000 000 000 is a milliard, and for Americans, the same number is a billion. A new name is given for every larger order of 1000. A number with 12 zeros will be a billion for Europeans and a trillion for Americans.
For Americans, the Latin roots of the numbers show the number of groups of 3-zeroes that follow 1,000. A number with 15 zeros will be a quadrillion.
Next, we’ll have quintillion, sextillion, septillion, octillion, nonillion, and decillion. Latin numerals are used for further numbers, and the number with 100 sets of 000 after 1,000 will be called a centillion.
For Europeans, however, the names such as trillion, quadrillion, and quintillion show the number of groups of 6-zeroes that follow 1. The number with 18 zeros (a quintillion for Americans) will be a trillion for Europeans.
Numbers that show the number of groups of 6-zeroes that follow 1000 have the suffix -iard: the number with 15 zeros will be a billiard, and the number with 21 zeros will be a trilliard.
White measuring tape – illustrative photo. Image credit: Diana Polekhina via Unsplash, free license
Why Do People Need Super Huge Numbers?
A trillion is nowhere close to being really big, at least in scientific areas. Super huge numbers (such as googol and googolplex which are described in two sections below) are not typically needed for everyday practical purposes. Instead, these extremely large numbers are used in mathematics, science, and theoretical contexts.
Here is what these extraordinarily big numbers bring to humanity:
- Theoretical Exploration: Mathematicians and scientists often work with large numbers to explore the limits of mathematical and computational systems. Investigating the properties and behaviors of numbers at extreme scales can help in the development of mathematical theories and computational algorithms.
- Conceptual Understanding: Large numbers are sometimes used to illustrate concepts related to scale, size, and orders of magnitude. They help people grasp the vastness or minuteness of certain quantities. For example, in cosmology, large numbers are used to describe the size and age of the universe.
- Representation of Possibilities: In probability theory and combinatorics, super huge numbers are used to represent the number of possible outcomes or combinations. For instance, when calculating the number of ways to arrange a deck of cards or the possibilities in quantum physics, these large numbers can be useful.
- Thought Experiments: Theoretical physics and cosmology often involve thought experiments that require considering extreme scenarios. Large numbers come into play when exploring ideas related to the nature of the universe, the behavior of particles, or the possibilities of extraterrestrial life.
- Mathematical Challenges: Large numbers are sometimes used in mathematical puzzles and challenges. These numbers can present intriguing problems for mathematicians and enthusiasts to explore.
- Illustrating Limits: Super huge numbers are sometimes used to illustrate the limits of our understanding or our computational capabilities. They demonstrate that certain calculations or measurements are beyond the practical scope of current technology or knowledge.
These extremely large numbers may not always have immediate practical applications in daily life. But they still play a vital role in advancing our understanding of mathematics, science, and the universe. They serve as tools for theoretical exploration, problem-solving, and conceptualization, helping researchers and scientists push the boundaries of human knowledge.
Mathematics often deals with large numbers such as a trillion and beyond. Image credit: Mika Baumeister via Unsplash, free license
What is a Googol?
There are also other fun names for numbers. For example, the so-called Googol.
Well, it has nothing to do with Google.
One googol is a mathematical term denoting one followed by 100 zeroes. And one googolplex is one followed by one googol zeroes.
It is an exceptionally large and almost incomprehensible number – although not the largest of them all.
The term “googol” was coined by the American mathematician Edward Kasner in the early 20th century when he asked his nine-year-old nephew, Milton Sirotta, to come up with a name for this extraordinarily large number. The word “googol” was the result of the child’s imagination.
To give you a sense of the scale of a googol, consider that there are estimated to be around 1080 atoms in the observable Universe. In comparison, a googol is vastly larger, demonstrating the vastness of mathematical concepts and the scale of numbers that mathematicians sometimes work with in theoretical and scientific contexts.
What is a Googolplex?
“Googolplex” is also a mathematical concept related to the famous googol name. But it is even larger.
A googolplex is 10 raised to the power of a googol, or 1 followed by a googol number of zeros. The number googolplex is so incredibly large that it exceeds the number of particles in the observable universe, making it practically impossible to represent or work with in any physical way.
In astronomy, numbers such as trillion and bigger are fairly common. Image credit: Piqsels, free licence
But Why do Americans and Europeans Use Different Names for Big Numbers?
The use of different names for big numbers between Americans and Europeans can be attributed to historical, linguistic, and cultural factors.
These differences are particularly notable when it comes to the naming of large numbers in the “long scale” used in many European countries and the “short scale” used in the United States and some other English-speaking countries.
The differences in naming large numbers trace back to historical practices and cultural influences. Different regions and languages have developed their own number naming systems over time.
In the so-called long scale, each new term represents one million times the previous term. In contrast, the short scale uses a thousand-fold increase for each new term.
For example, a billion in the long scale is equivalent to a trillion in the short scale. Meanwhile, a trillion in the long scale is equal to a quintillion in the short scale.
– In the Long Scale:
- Milliard = 1,000,000,000 (109)
- Billion = 1,000,000,000,000 (1012)
- Billiard = 1,000,000,000,000,000 (1015)
- Trillion = 1,000,000,000,000,000,000 (1018)
- Trilliard = 1,000,000,000,000,000,000,000 (1021)
- Quadrillion = 1,000,000,000,000,000,000,000,000 (1024)
– In the Short Scale:
- Billion = 1,000,000,000 (109)
- Trillion = 1,000,000,000,000 (1012)
- Quadrillion = 1,000,000,000,000,000 (1015)
- Quintillion = 1,000,000,000,000,000,000 (1018)
- Sextillion = 1,000,000,000,000,000,000,000 (1021)
- Septillion = 1,000,000,000,000,000,000,000,000 (1024)
Different languages have their own systems for naming large numbers, and these linguistic variations have influenced the number naming systems in different countries. For example, French and Spanish-speaking countries use the long scale, which has influenced the number naming conventions in Europe.
Cultural factors, including education systems and historical usage, play a role in which number naming system a country adopts. For example, the long scale was historically used in much of Europe, while the short scale was adopted in the English-speaking world.
The differences in naming large numbers can sometimes lead to confusion in international contexts. To mitigate this, international scientific and financial organizations often use standardized notations such as scientific notation (e.g., 10^9 or 109 for a billion) to ensure clarity and consistency.
The long scale today is also more prevalent in Europe, but not all European countries use it, and there can be variations within regions. Meanwhile, the short scale is used in many English-speaking countries beyond the United States, such as Canada and Australia.
Solving mathematical equations – illustrative photo. Dealing with trillions is a usual business in math and science. Image credit: ThisisEngineering RAEng via Unsplash, free license
These differences in naming large numbers are examples of how language and culture can influence mathematical conventions. The long scale, with each new term representing a millionfold increase, has deep roots in European languages and cultures. In contrast, the short scale, using a thousandfold increase for each new term, has become standard in the English-speaking world.
So now you know that the number that comes after trillion can have two different names: it is either a quadrillion (in the short scale) or a trilliard (in the long scale).
These differences can sometimes lead to confusion, especially in international contexts. To address this, international organizations often employ standardized notations like scientific notation, ensuring clarity and consistency across linguistic boundaries.
Written byGiedrius PakalkaandAlius Noreika