# What is the biggest 3 digit number in decimal system?

The method to represent and work with numbers is known as the number system. A number system is a system of writing to represent numbers. It is the mathematical notation used to represent numbers of a given set by using digits or other symbols. It allows us to operate arithmetic operations such as division, multiplication, addition, subtraction.

Some important number systems are as follows:

- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System

Let’s see about all these number systems in detail:

**Decimal Number System**

The decimal number system consists of ten digits i.e. from 0 to 9. The base of the decimal number system is 10. These digits can be used to represent or express any numeric value.

For example, the decimal number 153 consists of the digit 3 in ones place, the digit 5 in tens place and the digit 1 in hundreds place which can be represented as :

(1 × 10^{2}) + (5 × 10^{1}) + (3 × 10^{0})

= (1 × 100) + (5 × 10) + (3 × 1) { where, 10^{0} = 1}

= 100 + 50 + 3

= 153

**Binary Number System**

The binary number system consists of only two digits i.e. 0 and 1. The base of a binary number system is 2. The digital computer represents all kinds of data in a binary number system.

For example, convert 100112 into decimal number system.

(100112)^{2} = 1 × 2^{5} + 0 × 2^{4} + 0 × 2^{3} + 1 × 2^{2} + 1 × 2^{1 }+ 1 × 2^{0}

= 32 + 0 + 0 + 4 + 2 + 1

= (39)_{10}

**Octal Number System**

The octal number system consists of digits from 0 to 7. The base of an octal number system is 8. Octal number systems are basically used in computer applications.

For example, convert 1458 into decimal.

1458 = 1 × 8^{2} + 4 × 8^{1}+ 5 × 8^{0}

= 64 + 32 + 5

= 10110

**Hexadeciamal Number System**

In the hexadecimal number system, numbers are first represented from digits 0 to 9 as decimal number system, and then the numbers are represented using alphabets from A to F. The base of a hexadecimal number system is 16.

For example, convert 26BC16 to decimal.

26BC16 = 2 × 16^{3} + 6 × 16^{2} + 11 × 16^{1} + 12 × 16^{0}

= 8192 + 1536 + 176 + 12

= 991610

### What is the biggest 3 digit number in the decimal system?

**Answer:**

The highest three-digit number in the decimal is 999.

Explanation:If you add 1 to this number it becomes 1000 which is a four digit number. So 999 is the highest three digit number in the number system.Highest 3 digit number in the number system = 999

= > 999 + 1

= > 1000 (which is four digit number)

Hence it is proved that 999 is the highest three digit number in decimal system.

By this method you can find any greatest number in the number system.

**Sample Questions**

**Question 1: What is the smallest 1 digit number?**

**Answer: **

Smallest 1 digit number in the number system is 0.

**Question 2: What is the highest 1 digit number in decimal?**

**Answer: **

Highest 1 digit number in the number system 9.

**Question 3: What is the smallest 2 digit number?**

**Answer: **

Smallest 2 digit number in the number system is 10.

**Question 4: What is the highest 2 digit number in decimal?**

**Answer: **

Highest 2 digit number in the decimal number system 99.

**Question 5: What is the smallest 3 digit number?**

**Answer: **

Smallest 3 digit number in the number system is 100.

Explanation:if we subtract -1 from the number it becomes 2 digit number that is 99 (two-digit number). So 100 is the smallest 3 digit number in the number system.Smallest 3 digit number = 100

=> 100 – 1

=> 99 (Which is a 2 digit number)

So it is proved the 100 is the smallest 3 digit number in the number system.

**Question 6: What is the highest 4** **digit number in decimal?**

**Answer: **

Highest 3 digit number in the decimal number system is 9999.

Explanation – If we add +1 to the number (9999) it becomes 5 digit number that is 10000 (Four digit number). So 999 is the largest 3 digit number in the number system.

Largest 3 digit number = 9999

=> 9999 + 1

=> 10000 (Which is 4 digit number)

So it is proved the 9999 is the largest 3 digit number in the number system.

**Question 7: What is the smallest 5 digit number?**

**Answer: **

Smallest 5 digit number in the number system is 10000.

Explanation – if we subtract -1 from the number it becomes 4 digit number that is 9999 (Four digit number). So 10000 is the smallest 5 digit number in the number system.

Smallest 5 digit number = 10000

=> 10000 – 1

=> 9999 (Which is 4 digit number)

So it is proved the 10000 is the smallest 5 digit number in the number system.

**Question 8: What is the largest 5 digit number?**

**Answer:**

Largest 5 digit number in the number system 99999.

Explanation – If we add +1 to the number ( 99999 ) it becomes 5 digit number that is 100000 ( Six digit number ). So 99999 is the largest 5 digit number in the number system.

Largest 5 digit number = 99999

=> 99999 + 1

=> 100000 ( Which is 6 digit number )

So it is proved the 99999 is the largest 5 digit number in the number system.