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Reference

Types of Decimals

Concept

Decimal Numbers

Numbers that lie between integers on the number line can be written as decimal numbers. These consist of an integer part, a decimal point as a separator, and a non-zero decimal part written to the right of the decimal point. Consider the number as an example.
The decimal 12.346 where 12 is an integer part, . is a decimal point, and 346 is a decimal part
The integer part of this number is Since there is a decimal part, the number is greater than but less than Therefore, when plotting on a number line, the point will lie between and
It is important to note that these decimals can have very different values, depending on their place value.

Concept

Repeating Decimals

A repeating decimal number, or recurring decimal number, is a number in decimal form in which some digits after the decimal point repeat infinitely. The digits repeat their values at regular intervals and the infinitely repeated part is not zero. When writing the decimal, a line is drawn over the repeating portion to express such a number.

Repeating Decimal Numbers
Number Notation Fraction
Since they can be expressed as fractions, repeating decimal numbers are rational numbers.

Concept

Terminating Decimals

A terminating decimal number is a number in decimal form with a finite number of digits. Terminating numbers can be written as fractions, which means that they are rational numbers.

Terminating Decimal Numbers
Number Fraction
Additionally, if a decimal number has an infinite number of non-repeating decimal digits, it cannot be written as a fraction. Those numbers are considered irrational numbers.

Concept

Irrational Numbers

The set of irrational numbers is formed by all numbers that cannot be expressed as the ratio between two integers.
Irrational numbers are real numbers, but they cannot be expressed as fractions. Also, the decimal expansion of irrational numbers is not repeating and non-terminating.
In other words, a number is irrational if it is not rational. Although this number set does not have its own symbol, it is sometimes represented with a combination of other symbols.