20 Examples of Irrational Numbers

The numbers They are mathematical concepts that represent a certain quantity in relation to a unit. Within these mathematical expressions, rational and irrational numbers are identified:

  • Rational numbers. They are those that can be expressed as a fraction, with a denominator that is not zero. Basically it is the quotient of two numbers that are integers. For instance: 1/3, 2/4, 5/4.
  • Irrational numbers. As opposed to rational numbers, these cannot be expressed as a fraction because they have non-periodic decimal places in an endless or infinite way. For instance: √5, √685, √201, √609.

Examples of irrational numbers

  1. π (pi). It is the best known irrational number and it is the expression of the relationship that exists between the diameter of a sphere and its length. Pi equals 3.141592653589 (…), although it is generally known simply as 3.14.
  2. √5. 2.2360679775
  3. √123. 11.0905365064
  4. and. It is the Euler number and it is the curve that is observed in electrical tissues and that appears in processes such as radioactive radiation and growth processes. Euler’s number is: 2.718281828459 (…).
  5. √3. 1.73205080757
  6. √698. 26.4196896272
  7. Golden. This number is represented by the symbol Φ (which is the Greek letter Fi) and is also known as golden ratio, golden number, mean, golden ratio, among others. What this irrational number expresses is the proportion that exists between two parts of a line, either of something found in reality or of a geometric figure. It is a number widely used by visual artists when it comes to establishing proportions in their works. This number is: 1.61803398874989.
  8. √99. 9.94987437107
  9. √685. 26.1725046566
  10. √189. 13.7477270849
  11. √7. 2.64575131106
  12. √286. 16.9115345253
  13. √76. 8.71779788708
  14. √2. 1.41421356237
  15. √19. 4.35889894354
  16. √47. 6.8556546004
  17. √8. 2.82842712475
  18. √78. 8.83176086633
  19. √201. 14.1774468788
  20. √609. 24.6779253585

Irrational numbers in everyday life

Some of the uses of irrational numbers are:

  • Calculate circumferences. The irrational number π is used to calculate the circumference of a circle. For this, the formula C = πd is used in which the diameter is multiplied by the number pi. This function is essential for the manufacture of everyday items such as clocks, wheels and vinyl records. It is also used to make the geometric figures of a soccer field.
  • Build cylindrical structures. The irrational number π is used within the construction field to make cylinder-shaped structures. It is also used to make elements or goods with that shape, such as candles, rolls of paper, bottles, carafes, cans, among others.
  • Calculate volumes. The irrational number π is used to calculate the volumes of circular geometric figures. This is useful to know the content that this type of structure can contain.
  • Calculate compound interest rates. The irrational number e is used in the formula used to calculate continuous capitalization and forecast future capital based on initial capital and interest.
  • Calculate continued population growth. The irrational number e is used within the scope of biology to calculate continued growth in populations of living things. This formula is applied in the model of the English economist Thomas Malthus.
  • Calculate probabilities. The irrational number e is used within probability theory to determine the possible outcomes for a given event.
  • Create pieces of art and architecture. The irrational number Φ or golden ratio is used in architectural works, design and in photography because it is understood as a measure that alludes to beauty and the desired proportion. The golden ratio is present in phenomena or elements of nature, such as sunflower seeds or the shell of snails, and is based on the idea of ​​the golden rectangle (one that has sides that keep a golden ratio).
  • Create objects. The golden ratio is used to create everyday pieces based on the ratio measurements of the golden rectangle, such as credit cards. The golden ratio is also used to create advertisements, websites and logos.