Definition of repeating decimal

The term "repeating decimal" refers to a decimal number that goes on repeating itself in a cyclic pattern after a certain number of decimal places. The word "repeating" is used to describe this phenomenon because the decimal number seems to repeat itself as if it were on a loop, like a broken record. The concept of repeating decimals can be traced back to ancient civilizations like the Greeks and Indians, who used decimal fractions in their mathematics. However, the modern definition of a repeating decimal as we know it today emerged during the early 19th century when mathematicians began to study decimal fractions in greater detail. In 1813, the English mathematician Charles Babbage wrote about repeating decimals in his book "Works Concerning the Political Economy". Babbage explained that certain decimal fractions that appeared to be irrational, or without repeating patterns, actually concealed repeating patterns that were too complex to be noticed by the human eye. He introduced the term "repeating decimal" to describe these numbers. The concept of repeating decimals gained wider recognition in the 19th century thanks to the development of decimal arithmetic, which made it easier to manipulate decimal numbers. Decimal fractions were especially important in the context of commerce, where they were used to calculate prices and volumes of goods in a more convenient and accurate way than was possible with traditional fractions. Today, the concept of repeating decimals is a fundamental part of mathematics and is taught in primary and secondary schools around the world. Repeating decimals play an important role in areas such as finance, engineering, and computer science, where they are used to represent fractions and decimal values with high accuracy.