Irrational numbers cannot be expressed as a fraction or a full decimal. Examples include pi, the square root of two, Euler’s number, and the golden ratio. They are used in equations and can be difficult to use on basic calculators. Mathematicians study these numbers for their intriguing properties and potential applications.
Irrational numbers are numbers that cannot be expressed as a fraction and which are also impossible to record as a full decimal. People have been working with irrational numbers since Greek and Roman times, and a number has been identified by mathematicians over the centuries. There are a number of interesting applications and uses for irrational numbers, ranging from frustrating math students to completing complex equations.
So-called rational numbers can all be written in decimal form or as a fraction. ¾, for example, is a rational number, which can also be expressed as .75. When a number is irrational, it cannot be written as a fraction with whole numbers and the number will be impossible to record in decimal form. Pi is a famous example of an irrational number; while it is often simplified to 3.14 for the purpose of rough calculations, pi cannot actually be written completely in decimal form because the decimal is infinite.
Some other examples include the square root of two, Euler’s number, and the golden ratio. For simplicity, some of these numbers are written as symbols, such as the “e” for Euler’s number, and will sometimes be represented in partial decimal form. When an irrational number is presented in decimal form, ellipses are usually used after the last decimal number to indicate that it continues, as in 3.14… for pi.
People often start working with these numbers at a young age, even though they may not be specifically introduced to the concepts of rational and irrational numbers until later. Pi is one of the first irrational numbers many people learn, because it’s used in equations to find the area and circumference of a circle, and these equations often make an excellent introduction to more advanced math for young children. People are also introduced to the concept in many of the sciences as they start learning about the equations that are commonly used.
These unusual numbers can be difficult to use on a basic calculator, due to the calculator’s limitations. It is usually necessary to have an advanced scientific or graphing calculator that has been programmed with these numbers and their values.
Some mathematicians make studying these numbers their life’s work. These numbers often have a number of intriguing properties that are fun for people who love math to explore, and a mathematician might even be able to come up with a new application for an irrational number.
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