Identify all the sets to which the number 3.1214122144 belongs
To identify all the sets to which the number 3.1214122144 belongs, we need to understand the properties and characteristics of different number sets. Let's go through some common number sets:
1. Natural numbers (N): Natural numbers are counting numbers starting from 1 and going infinitely without including zero (0), negative numbers, or decimal fractions. Since 3.1214122144 is not a counting number, it does not belong to the set of natural numbers.
2. Whole numbers (W): Whole numbers include all the natural numbers (counting numbers) and zero (0). As 3.1214122144 is neither a counting number nor zero, it does not belong to the set of whole numbers.
3. Integers (Z): Integers consist of all the whole numbers (counting numbers and zero) along with their negative counterparts. Since 3.1214122144 is not an integer, it does not belong to this set.
4. Rational numbers (Q): Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. This includes integers and fractions. Since 3.1214122144 is not a fraction or integer, it does not belong to the set of rational numbers.
5. Real numbers (R): Real numbers are a set that includes all rational numbers (integers, fractions) and irrational numbers. Irrational numbers cannot be expressed as fractions and go on infinitely without repeating. To determine if 3.1214122144 is a real number, we need to check if it is rational or irrational.
To check if 3.1214122144 is rational or irrational, we can use the decimal representation. If the decimal representation repeats or terminates, it is rational; otherwise, it is irrational.
3.1214122144 is a decimal that does not repeat or terminate. Therefore, it is an irrational number. Since irrational numbers are a subset of real numbers, we can conclude that 3.1214122144 belongs to the set of real numbers (R) and irrational numbers (I).