Is pi/2 a rational number?
Understand the Problem
The question is asking whether the value of pi divided by 2 (Ï€/2) is a rational number or not. A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Answer
$ \frac{\pi}{2} $ is an irrational number.
Answer for screen readers
The value of $ \frac{\pi}{2} $ is an irrational number.
Steps to Solve
- Definition of rational numbers
First, recall that a rational number can be expressed as $ \frac{a}{b} $ where $a$ and $b$ are integers, and $b \neq 0$.
- Consider the value of $\pi$
The value of $\pi$ (pi) is known to be an irrational number. This means that it cannot be expressed as a fraction of two integers.
- Finding $\frac{\pi}{2}$
Now, we need to consider the expression $ \frac{\pi}{2} $. Since $\pi$ is irrational, we will check if dividing it by 2 changes its nature.
- Determining the nature of $\frac{\pi}{2}$
Dividing an irrational number by a non-zero integer (in this case, 2) results in another irrational number. Therefore, since $\pi$ is irrational, $ \frac{\pi}{2} $ must also be irrational.
The value of $ \frac{\pi}{2} $ is an irrational number.
More Information
The number $ \pi $ is approximately $3.14159$ and is commonly used in mathematics, particularly in geometry to represent the ratio of a circle's circumference to its diameter. The dividing of irrational numbers by rational numbers yields irrational results.
Tips
- A common mistake is to assume that dividing any real number by an integer results in a rational number. Remember, this doesn’t apply to irrational numbers.
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