## Cardinal Numbers and Ordinal Numbers

Cardinal numbers and ordinal numbers are explained here with the help of colorful pictures.

There are many steps in a staircase as shown in the above figure. The given staircase has nine steps, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9.

In the process of climbing up the stairs, we term step Number (1) as the **first** step, step Number (2) as the **second** step number (3) as the **third** step, Number (4) as the **fourth** step, Number (5) as the **fifth** step, Number (6) as **sixth** step, Number (7) as **seventh** step, Number (8) as **eighth** step and Number (9) as **ninth** step. These are also expressed as 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, 5^{th}, 6^{th}, ………… etc.

Numbers 1, 2, 3, 4, 5, ……, 9, etc., are called **cardinal numbers** while 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, 5^{th}, 6^{th}, ………… etc., are known as **ordinal numbers**.

The cardinal numbers express the quantitative property of the numbers while the ordinal numbers express their order. The cardinal numbers express the number of objects in a collection while the ordinal number always expresses one object.

**For example**, there are five students in a row (cardinal number) and fifth student of the row (ordinal number).

While coming down the stairs the ordinal numbers are changed. The 9^{th} becomes the 1^{st}, the eighth becomes 2^{nd}, the seventh becomes 3^{rd} and so on. Thus, ordinal numbers are changed in reverse order, i.e., the last becomes the first, the last but one becomes the second, etc. But the cardinal numbers remain the same.

Cardinal numbers

showing serial number

**⇒** 1 2 3 4 5 6 7 8 9

of steps of staircase

Ordinal numbers

from **⇒** 1^{st} 2^{nd} 3^{rd} 4^{th} 5^{th} 6^{th} 7^{th} 8^{th} 9^{th}

the front

Ordinal numbers

from **⇒** 9^{th} 8^{th} 7^{th} 6^{th} 5^{th} 4^{th} 3^{rd} 2^{nd} 1^{st}

the back

Thus, the ordinal numbers indicate the position of an object from the front or back of any given object.

Let us imagine that, there are seven boys in a row who are numbered as 1, 2, 3, 4, 5, 6 and 7 from one end of the row. These numbers are called cardinal numbers.

**For example:**

● *Ordinal Numbers from 1 to 7: * 1^{st} 2^{nd} 3^{rd} 4^{th} 5^{th} 6^{th} 7^{th}

● *Ordinal Numbers from 7 to 1:* 7^{th} 6^{th} 5^{th} 4^{th} 3^{rd} 2^{nd} 1^{st}

Now if we take the position of each boy from boy number (1). The position of each boy is indicated by ordinal numbers. These are from left to right as 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, 5^{th}, 6^{th}, 7^{th} and from right to left as 7^{th}, 6^{th}, 5^{th}, 4^{th}, 3^{rd}, 2^{nd}, 1^{st}.

Thus, from both sides the position of each boy may be indicated by ordinal numbers.

2nd Grade Math Practice

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