CIRCULATING DECIMAL Meaning and
Definition
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A circulating decimal refers to a decimal representation of a rational number in which there is a repeating block of digits that continues indefinitely. It is a decimal that repeats a sequence of numbers or a group of digits over and over again. The repeating block is enclosed in a bracket called a vinculum. For example, in the circulating decimal 0.666..., the digit 6 recurs indefinitely, and thus the number can be written as 0.6̅.
Circulating decimals are commonly encountered in fractions that have a non-terminating decimal representation. When converting a fraction to a decimal, if the denominator is not a factor of 10 or any power of 10, the result will be a circulating decimal. The length of the repeating block in a circulating decimal depends on the prime factors of the denominator. For instance, a fraction with a denominator that only contains 2 or 5 as prime factors will result in a terminating decimal.
Circulating decimals can be represented using a general notation where the recurring block is indicated using a horizontal line above the digits that repeat. This notation is particularly useful when dealing with algebraic calculations involving recurring decimals. It is important to note that the vinculum is not to be confused with a decimal point, as it represents distinct mathematical operations.
Overall, circulating decimals exhibit a distinct pattern of repeating digits, making them a distinctive representation of certain rational numbers within the decimal system.
Common Misspellings for CIRCULATING DECIMAL
- xirculating decimal
- virculating decimal
- firculating decimal
- dirculating decimal
- curculating decimal
- cjrculating decimal
- ckrculating decimal
- corculating decimal
- c9rculating decimal
- c8rculating decimal
- cieculating decimal
- cidculating decimal
- cifculating decimal
- citculating decimal
- ci5culating decimal
- ci4culating decimal
- cirxulating decimal
- cirvulating decimal
- cirfulating decimal
Etymology of CIRCULATING DECIMAL
The etymology of the term "circulating decimal" can be understood by breaking down the constituent words.
1. "Circulating" originates from the Latin word "circulatus", which means "to go round in a circle". It is derived from the Latin noun "circulus", meaning "circle" or "ring". In the context of decimals, "circulating" refers to the repetition or circular pattern of digits in a decimal.
2. "Decimal" is derived from the Latin word "decimus", which means "tenth". It is derived from the Latin noun "decem", meaning "ten". "Decimal" is used to describe the numbering system based on powers of ten, where fractions are expressed in increments of tenths, hundredths, thousandths, etc.
Similar spelling word for CIRCULATING DECIMAL
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