During this week in Precalc 11, I learned more about number types. I was familiar with the different number types there are as we have talked about them in Math 10 but I was never confident. I understood all of them this week and can now successfully and confidently identify them.

To start, we need to identify that there are 6 different number types, now there might be more but this is what we are working with in this unit. These 6 different number types are Real, Irrational, Rational, Integers, Whole, and Natural. This order I put them is in descending order. We also need to remember that these numbers have symbols that represent them. Let’s start with the easiest…

Natural  

• Natural numbers are numbers that our parents taught us. They are the easiest and most simple to work with.
• In natural numbers there is no 0 only positive whole numbers. 
• example: 1,2,3,4,5……
• Symbol: N

Whole 

• Whole numbers are similar to natural numbers BUT they include zero. 
• example: 0,1,2,3,4,5…..
• Symbol: W

Integers 

• Integers are a little more different, they are whole numbers but they include the negatives. 
• example: ….-3,-2, -1, 0, 1, 2, 3…..
• Symbol: I

Rational 

• rational numbers are where it gets a little more complicated (at least for me).
• rational numbers can be made by dividing an integer by an integer. like so 👉 a/b    a and b = integers  but b does not += 0
• rational numbers are repeating like 0.36666666…..
• but also rational numbers end at some point like 1.3475
• It is good to remember that rational numbers are ugly numbers that are created by dividing.
• symbol: Q

Irrational 

• irrational numbers are different from rational
• irrational numbers do not repeat at all so they are unpredictable 
• they also do not end
• example: Pi, 0.387539821…
• Symbol: ō (Q with a line on top)

Real 

•  real numbers are the biggest category and that’s because they include everything
• so if something is natural it is also real. or if something is irrational it is also real.
• Symbol: R

You have to remember that a number can be more than one type. for example, 0 is W, I and also R.  but also remember that irrational numbers are very specific and they do not fit this statement. for example, -789 is N, W,I and R but it cannot be irrational.

Here is a drawing to help visualize