cardinal numbers, ordinal numbers

We use numbers to express some quantity, measurement, to tell the amount of something. For instance, how many candies do we have? How old are we? Also, we use numbers to tell some positions, for instance, what place we are in a race? Or which floor do we live in? As well as, to tell when our birthday is. But, have you ever noticed that something is different, depending on what we are talking about? We say that we have 5 (five) candies. But we say that we live on the 5^th (fifth) floor. Let's see why is that? In math, we have two types of numbers, that we should use accordingly on what we want to express. They are called cardinal and ordinal numbers. Learning about these types of numbers and when to use them appropriately is very important. We will not be expressed correctly, or understood by others if we say "I have 5^th (fifth) candies" or "I live on five floor."

Cardinal numbers

Cardinal numbers should be used when we are counting something, for instance, how many children are in the classroom, how many candies someone has, or how many flowers are in a vase. They have to be whole counting numbers (1, 2, 3, 4, 5, 6, 7, 8, and so on). Cardinal numbers are used to count a set of objects and tell us about quantity. As they are used to count sets of objects, they are sometimes referred to as 'counting numbers'  These numbers include one (1), two (2), three (3), four (4), five (5), and so on.

Examples: 

1. There are twenty-three (23) students in the classroom.
2. She has five (5) candies.
3. There are seven (7) flowers in the vase.

Ordinal numbers

We use ordinal numbers to talk about the "order" of things or to define a thing's position in a series. Ordinal numbers do not indicate quantity as cardinal numbers do. They are used to show the place of a thing in a list. We use ordinal numerals to express the position or rank of something in sequential order of size, chronology, importance, for example, first (1^st), second (2^nd), third (3^rd), fourth (4^th), fifth (5^th), sixth (6^th), and so on. 

Examples: 

1. He is third (3^rd) in the race.
2. It is my second (2^nd) piano lesson. 
3. She lives on the fifth (5^th) floor.

Dates are another example of ordinal numbers:

• Angela's birthday is on the nineteenth (19^th) of March.
• It is the twenty-first  (21^st) century now.

Below is a chart of cardinal and ordinal numbers from 1 to 10.

Cardinal numbers	Ordinal numbers
1 (one)	1st (first)
2 (two)	2nd (second)
3 (three)	3rd (third)
4 (four)	4th (fourth)
5 (five)	5th (fifth)
6 (six)	6th (sixth)
7 (seven)	7th (seventh)
8 (eight)	8th (eighth)
9 (nine)	9th (ninth)
10 (ten)	10th (tenth)

Each ordinal associates with one cardinal, its cardinality. 

***Tips to remember:

• We use cardinal numbers when we are counting.
• Cardinal numbers have to be whole, counting numbers
• Cardinal numbers are sometimes referred to as 'counting numbers'.
• We use ordinal numbers when we are ordering, positioning things or numbers.
• We use ordinal numbers to represent dates.
• Each ordinal associates with one cardinal, its cardinality.