Identify all the sets to which the number 3.121412214 4... Belongs
To identify all the sets to which a number belongs, we need to categorize it based on its properties. Let's analyze the number 3.121412214 4... and determine the sets it belongs to:
1. Rational Number Set: A rational number is any number that can be expressed as a fraction of two integers. Since 3.121412214 4... can be written as 3121412214/10^9, where both the numerator and denominator are integers, it belongs to the set of rational numbers.
2. Real Number Set: The real number set encompasses all rational and irrational numbers. Since 3.121412214 4... is not an integer or a fraction and its decimal representation continues indefinitely without repeating, it is an example of an irrational number. Therefore, it also belongs to the set of real numbers.
3. Decimal Number Set: Decimal numbers are a way to represent real numbers by expressing them in terms of units, tenths, hundredths, thousandths, and so on. 3.121412214 4... is a decimal number because it has digits after the decimal point, making it a member of the decimal number set.
4. Terminating Decimal Set: A terminating decimal is a decimal number that ends after a finite number of digits. Since 3.121412214 4... has an infinite number of digits after the decimal point, it does not belong to the set of terminating decimals.
5. Non-terminating and Non-repeating Decimal Set: A non-terminating, non-repeating decimal is an irrational number whose decimal representation does not end and does not have a repeating pattern. Since 3.121412214 4... fits this definition, it belongs to the set of non-terminating and non-repeating decimals.
In summary, the number 3.121412214 4... belongs to the sets of rational numbers, real numbers, decimal numbers, and specifically, the subsets of irrational numbers and non-terminating non-repeating decimals.