numbers

Numbers are everywhere around us. They are connected to everything we do. Numbers help us understand the world around us and have a presence in almost all the activities that we perform in our everyday life. Numbers are used for counting, measuring, and keeping things in order... Let us see how. 

	For example, this packet of chocolate cost $10.
	For example, my weight is 45 kilograms.
	For example, Jane is 152 centimeters tall.
	For example, my phone number is 001345678.
	For example, the distance between my house and the school is 6 kilometers.
	For example, I wake up at 6:00 in the morning and get ready for my school.

A number system is a writing system for denoting numbers using digits or symbols in a logical manner. We use the digits 0,1, 2, 3, 4, 5, 6, 7, 8, and 9 to form all numbers. This number system using 10 digits is called the Decimal Number System or Base-10 system. With the help of these digits, we can create infinite numbers. Digits are numeric symbols, and with their combination, we can write all the numbers we can think about.
How do we use these 10 digits - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for writing numbers? Let us find out below!

1.    I am 12 years old. 
To write the number of years, we use the number 12, for which we use two digits, 1 and 2.
2.    I have $20.
To write the amount of money we have, we use the number 20, for which we use two digits, 2 and 0.
3.    In the Solar System, there are 8 planets.
To write the number of planets, we use the number 8, for which we use one digit, digit 8.

What are Number Names?

Number names are a way in which we can represent numbers in word form. For example, we can use the word “one“ to represent the number “1“, we can use the word “two“ to represent the number “2“  and so on. In this way, we can represent any number in word form which is known as the number name for the number. Let us try writing the number names for the above examples. Please go through the below table to see how numbers are replaced with their number names:

I am 12 years old.	I am twelve years old.
I have $20.	I have twenty dollars.
In the Solar System, there are 8 planets.	In the Solar System, there are eight planets.

One two and three-digit numbers

We know that all the numbers are formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. Some numbers are formed with one digit, some with two digits, and some with many digits.

• There are 9 numbers of one digit. The smallest one-digit number is 1 and the greatest one-digit number is 9.  

• There are 90 numbers of two digits. The smallest two-digit number is 10 and the greatest two-digit number is 99.

How many two-digit numbers can you form using digits 3 and 7? Answer: You can form 2 two-digit numbers using digits 3 and 7, they are 37 and 73.

• Next to the number 99 is the number 100, which is the smallest three-digit number. As you can see, the digits needed for this number are 1, 0, and 0.  Next are 101, 102, 103, 104, and 105, and continue till 999, which is the greatest three-digit number. 

• There are 900 numbers having three digits. The smallest three-digit number is 100 and the greatest three-digit number is 999.

• After three-digit numbers, next comes the four-digit numbers and then the five-digit numbers, and this series can continue till infinity!

Arrangement of digits to form numbers

We can form different numbers by rearranging the same set of digits. For example, you can create 24 different numbers using only 4 digits!

Digits 1, 7, 4, and 2 can form numbers like 1274, 1427, 2741, etc. Here we are considering the cases where we use distinct digits to create numbers, without repetition. 

Now we will learn how to create the smallest and the biggest number using the same set of digits. Let us take an example, use digits 1, 7, 4, and 2 to form the smallest and biggest number.  

To get the smallest number, we write the smallest digit at the extreme left, then the digits are placed to the right of it, from smallest to greatest, till we get a four-digit number. As in the above example, 1247 is the smallest number. How?

Step 1: Start with the leftmost position. 1 is the smallest digit. Hence our number starts with 1.

1

Step 2: The next smallest digit is 2 and is therefore written next to 1.

1

2

Step 3: Out of the two digits, that are left, 4 and 7, the digit 4 is the smaller one. We write it next to the digit 2.

1

2

4

Step 4: The biggest digit in this set is digit 7, and it fills the last position.

1

2

4

7

The smallest number using digits 7, 1, 2, and 4 is 1247.

To get the greatest number, we write the greatest digit at the extreme left, then the digits are placed to its right, from greatest to smallest, till we get a four-digit number.

In this case, using the same digits, but positioning them differently, we got the greatest number, which is 7421.

Note: If one of the digits is 0, it is not written at the extreme left. As 0 at the left-most position in a number does not have any value, therefore, the value of '11', '011', and '0011' are all same, which is 11. For example, when creating a three-digit number using the digits 1, 0, and 2, the smallest number cannot be '012' because the leading 0 has no value, making '012' equivalent to '12'. Therefore, the smallest valid three-digit number using 1, 0, and 2 is '102'.

Form two-digit numbers using digits 4 and 0. Answer: The only two-digit number that can be formed using 4 and 0 is 40.

Place Value

Now we understand that numbers are created using a combination of digits. We also know that 12 comes before 21 in the number series, i.e. 12 is smaller than 21, or 21 is greater than 12. 
What makes 21 greater than 12? It is the position of the digits in a number that makes its value bigger or smaller. Place value is the value of each digit in a number. 

Here place value of 2 in the number 21 is '20' and the place value of 2 in the number 12 is '2' (check where 2 is positioned in both numbers). You will learn more about place value in another lesson.

Activity time!

1. How many numbers can you form using digits 2, 5, and 7? 
2. Find the largest and the smallest number using digits 2, 5, and 7.
   

Answer:

1. We can form a total of 6 numbers by rearranging the given three digits 2, 5, and 7. They are 257, 275, 572, 527, 752, and 725. 
    
2. The smallest number is 257, and the largest number is 752.

2

5

7

 

7

5

2