# Irrational Numbers Worksheets

**What are Irrational Numbers?** Any number that can eb expressed as fraction like p/q for any integer p and q is called an irrational number. Irrational number have decimal expansions that nor become periodic or get terminated. Every number that is transcendental is an irrational number.
Another way of defining it is that irrational number cannot be expressed as ratio of two whole numbers. This is supposed to rational numbers like one-fifth, 2, 7, and -13/9, which are and can be expressed as the ration two whole numbers. When it is expressed as a decimal, a rational number go on forever after placing a decimal point and never gets repeated.
There is not any standard notation for irrational numbers but the notations R/Q where the bar, backslash or the minus sign indicates the set of rational number complement.
One of the most famous rational number is Root of 2 which is often called the Pythagoras theorem. It is said that the Pythagorean philosopher used the geometric method for demonstrating root 2 irrationality and notifying the comrades about it.
The funky numbers that make you look twice. These sheets will help you better understand what you are up against.

- Approximations of Irrational Numbers - These worksheets help you begin to understand the true value of an irrational value.
- Calculating Distance in the Complex Plane - This puts these values to work for you so you can see some direct application opportunities for using it.
- Conjugates and Dividing Complex Numbers - This is a more advanced form of these values found within operations.
- Graphing Complex Numbers - This brings these values to life in a visual form.
- Irrational Numbers and Decimal Expansion - This mostly applies to values undergoing a root.
- Multiplying and Adding Rational and Irrational Numbers - These operations can be tricky, if you aren't careful.
- Ordering For Rational Numbers - Sorting and ordering values properly demonstrates that you truly understand its value.
- Rational and Irrational Numbers - You can clearly see the difference between the two here.
- Simplifying Complex Numbers - I would suggest you take time to plan how you will approach each problem.
- Working with Absolute Value - These are more real-life situations.

### How Do Irrational Numbers Help Us in Real Life?

As we sit in math class, we often think that our teachers are simply trying to puzzle us everyday, and it is often difficult to see the purpose behind learning some forms of complex math. This topic is definitely one of those subject areas where students cannot see any purpose for in real life. That is because at its root this is completely conceptual math.

Irrational numbers help us create mathematical models that would never be possible with real numbers. These models simplify what can occur in a relationship or interactions that we cannot physically see. These values are not perfect, but they give us a glimpse into what we are unsure of.

One of the most famous irrational numbers has its own informal holiday. Pi (ℼ) day occurs every March 14 (get it 3.14). This constant models the ratio of the circumference of any circle to the diameter of the same circle. When I say any circle, I mean anything circular in shape. That would include things like car tires, frisbees, hockey pucks, baseballs. Engineers use this same constant to calculate the gripping power of tires that they are manufacturing. When it comes to working with anything that shape, it is hard not to rely heavily on this concept.