# What is the greatest 4-digit number?

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.

### Types of Number systems

The number system can exist for any base and it can have those number of digits involved accordingly. 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 a 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 one place, the digit 5 in the 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, 100 = 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 the binary number system is 2. The digital computer represents all kinds of data in a binary number system. For example, convert 100112 into a decimal number system.

(100111)_{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 the octal number system is 8. Octal number systems are basically used in computer applications. For example, convert 1458 into decimal.

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

= 64 + 32 + 5

= 10110

**Hexadecimal Number System**

In 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 the hexadecimal number system is 16. For example, convert 26BC16 to decimal.

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

= 8192 + 1536 + 176 + 12

= 991610

### The Greatest Four digit number

The greatest four-digit number can be expressed as the number with a digit at ones place, tenth place, hundredth place, and thousand place. All the digits have been the largest digits, in essence, 9.The Greatest four-digit number in the number system is ⇢ **9999**

**Explanation: **If 1 is added to this number, it becomes 10000 which is a five-digit number. So 9999 is the greatest four-digit number in the number system.

Greatest four digit number in the number system = 9999

= 9999 + 1

= 10000 ( which is five digit number )

Hence it is proved that 9999 is the greatest four-digit number.

**By this method**,** it is easy to find any greatest number in the number system.**

### Similar Questions

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

**Answer:**

The greatest 1 digit number in the number system is 9.

**Question 2:** **What is the 2 digit greatest number?**

**Answer: **

The greatest 2 digit number in the number system is 99.

**Question 3:** **What is the 3 digit greatest number?**

**Answer:**

The greatest 3 digit number in the number system is 999.

**Question 4: What is the 4 digit greatest number?**

**Answer:**

The greatest 4 digit number in the number system is 9999.

**Question 5:** **What is the 5 digit greatest number?**

**Answer: **

The greatest 5 digit number in the number system is 99999.

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