 GeeksforGeeks App
Open App Browser
Continue

# 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,

1. Decimal Number System
2. Binary Number System
3. Octal 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,

(1×102) + (5×101) + (3×100)

= (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 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20

= 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 82 + 4 X 81+ 5 X 80

= 64 + 32 + 5

= 10110

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 6 X 162 + 11 X 161 + 12 X 160

= 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?

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

Question 2: What is the 2 digit greatest number?

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

Question 3: What is the 3 digit greatest number?

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

Question 4: What is the 4 digit greatest number?