True or false
An irrational number is always a real number.
true
review the subsets of real numbers
True. An irrational number is always a real number.
To understand why, let's break it down:
1. Real numbers: Real numbers are numbers that can be represented on the number line. They include rational numbers (numbers that can be written as fractions) and irrational numbers (numbers that cannot be written as fractions).
2. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. They have non-repeating, non-terminating decimal representations. Examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler's number).
Since irrational numbers cannot be expressed as fractions, they don't fit the definition of rational numbers. However, they still exist on the number line and can be plotted as points, making them real numbers. So, it is true that an irrational number is always a real number.