Yes, every rational number is a real number.
Understanding Rational and Real Numbers
- Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Examples include 1/2, 3/4, -2/5, and 7.
- Real numbers encompass all numbers that can be plotted on a number line. This includes rational numbers, irrational numbers (like pi and the square root of 2), and zero.
The Relationship Between Rational and Real Numbers
Since every rational number can be expressed as a fraction, it can also be plotted on a number line. This means that every rational number is a real number.
However, not every real number is a rational number. Irrational numbers, which cannot be expressed as a fraction, are also part of the real number system.
Visualizing the Relationship
Think of the real number system as a large container. Inside this container are all the rational numbers, which form a smaller subset. The rest of the container is filled with irrational numbers.
