Can you count the stars of the universe without numbers or can you tell your age to someone without numbers? No! Because everything is just a game of numbers. Let us now see the general form of a number. Let us do it right away.

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## General Form of a Number

### Two-Digit Numbers

Let us first start with two digit numbers. In general, any two digit number ab can be written as,

ab = 10 × a + 1 × b = 10a + b

where a is a ten’s place digit and b is a unit’s place digit. Let us consider the example of a two digit number- 67. Now when we start from the right i.e from 7 to 6, the place of seven is known as *ones* and that for 6 is known as *tens.*

### Three-Digit Numbers

In general, any three-digit number xyz can be written as,

xyz = 100 × x + 10 × y + 1 × z = 10x + 10y + z

where, x is a hundredth place digit, y is a ten’s place digit and z is a unit’s place digit. Hence, if it’s a three digit number, the places will be ones, tens and *hundreds* from right to left.

Similarly, for a 4 digit number, it’ll be ones, tens, hundreds and *thousands*. For a five digit number, the leftmost place will be called* ten thousand*. Let’s understand this concept.

## Games with Numbers

### Reverse Three Digit Numbers

The difference between a 3-digit number and a number obtained by reversing its digits is always divisible by 11. Let 3-digit numbers be:

xyz = 100x + 10y + z

Reversing the order of digits we get,

zyx = 100z + 10y + x

On substraction, if x > z then difference between the numbers is

(100x + 10y + z) – (100z + 10y + x)

= 100x + 10y + z – 100z + 10y + x

= 99x – 99z → 99 ( x-z)

In case of z > x

(100z + 10y + x) – (100x + 10y + z)

= 100z + 10y + x – 100x + 10y + z

= 99z – 99x

= 99 (z-x)

In case of x =z the diffrence is zero.

### Forming Three-Digit Numbers from Given Three Digits

Example: Find the smallest three-digit number from the given digits 0, 7,8

Solution: Arrange the given digits in ascending order (as the smallest three-digit number) we have 0 < 7 < 8. Now as the number is a three digit number hence we cannot choose the first digit of the resultant to be 0 as it will make the number a two digit (say 078), hence the required number is 708

### Forming a Four Digit Number from Given Four Digits

Example: Find the largest four-digit number from the given digits 0, 7,8,6

Solution: Arranging the digits in descending order we get 8> 7 >6 > 0. Now the resultant is a four-digit number hence we cannot choose the first digit of the resultant to be 0. Hence the answer is 8760 choosing the digits of the resultant number in descending order.

### Letters for Digits

Here we have puzzles in which letters take the place of a digit in arithmetic sum and the problem is the to find out which letter represents which digit. There are two rules we follow while doing such puzzles.

- Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter.
- The first digit of a number cannot be zero.
- Thus, we write the number sixty-three as 63 and not as 063 or 0063.

For example, R and Y can be represented by 18 and 25 respectively, as per their alphabetical sequence.

## Solve Examples for You

**Question 1: On multiplying 121 and its reverse, we get**

- 14641
- 14541
- 14441
- None of the above.

**Answer:** A is the correct option. The reverse of 121 is 121, hence 121 × 121 = 14641.

**Question 2: Which of the numbers are in general form?**

- 2 × 100 + 3 × 10 + 7
- 2 × 10 + 3× 10 + 7
- 2 × 100 + 2 × 100 + 7
- 2 × 100 + 3 × 10 + 7

**Answer:** A is the correct option. The general form of any three digits is

abc = a× 100 + b × 10+ c

So, 237 = 2 × 100 + 3 × 10 + 7

So only one expression is in general form.

**Question 3: Can we say that 70 is a number?**

**Answer:** One can regard the number 70 as a natural number. Furthermore, 70 is a whole number that is without a fraction. Moreover, one can regard 70 is a “counting number”. Also, 70 is an even and composite number. Another categorization of 70 can be as a real number. 70 also happens to be a rational number.

**Question 4: What are the possible natural numbers that exist from 1 top 100?**

**Answer:** The natural numbers from 1 to 100 are all the numbers from 1 to 100, including 1 and 100 themselves. Furthermore, when we count from 1 to 100, all the numbers that one counts, without any exception, are natural numbers.

**Question 5: What is the number 1 and its fundamental property?**

**Answer: **1 is a number or numerical digit that is representative of a single entity. For example, if there is a line segment of unit length then it means that it means that it has a length of 1. Furthermore, multiplicative identity is a fundamental property of 1.

**Question 6: Explain why number 1 is unique?**

**Answer:** 1 is unique because it is neither a composite number nor a prime number.

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