What do you do to check whether a number is rational or irrational? In your explanation, use an example of an irrational and a rational number.
How do I explain or do this?!?
THE Hell? The second Ms. Sue you need to fricken leave Ms. Sue and other students on here ALONE.
http://www.mathsisfun.com/irrational-numbers.html
Thank you Ms.Sue!
You're welcome, Emma.
Mani, u a total idiot XD "Ms. Sue" could be ANYONE ON EARTH THAT JUST WRITES THE NAME IN THE NAME BOX MAN!!!!! I
ms sue was on many questions and is very annoying, never trust "her"
@ Right answers
Mani literally only cussed once, plus the "THE Hell?" part was probably on caps for "THE" accidentally.
To check whether a number is rational or irrational, you can follow a few methods. Let's start by understanding the definitions of rational and irrational numbers:
1. Rational Number: A number that can be expressed as a fraction p/q, where p and q are integers (q ≠ 0).
2. Irrational Number: A number that cannot be expressed as a fraction and whose decimal representation goes on infinitely without repeating.
Now, let's take an example of an irrational number such as √2.
1. Rational or Irrational?:
To determine if √2 is rational or irrational, we can assume that it is rational and express it as a fraction. Assuming √2 = p/q, where p and q are integers with no common factors, we square both sides to get the equation: 2 = (p^2)/(q^2). Rearranging, we get p^2 = 2q^2. This implies that p^2 is even, thereby making p even as well. If p is even, we can substitute p = 2k (where k is an integer) into the equation, resulting in (2k)^2 = 2q^2, which simplifies to 4k^2 = 2q^2. Dividing both sides by 2, we obtain 2k^2 = q^2. This shows that q^2 is also even, hence making q even too. If both p and q are even, it contradicts our assumption that p and q have no common factors. Therefore, we conclude that √2 cannot be expressed as a fraction, and it is an irrational number.
Now, let's examine an example of a rational number, such as 3.75.
2. Rational or Irrational?:
To determine if 3.75 is rational or irrational, we need to express it as a fraction. We can represent 3.75 as the fraction 375/100. Since both 375 and 100 are integers, and 100 is not zero, we can conclude that 3.75 is a rational number.
To summarize:
- The example of √2 demonstrates an irrational number because it cannot be expressed as a fraction.
- The example of 3.75 illustrates a rational number because it can be expressed as a fraction.