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Write the smallest and the largest six digit numbers in the Number System

  • Last Updated : 13 Oct, 2021

The method to represent and work with numbers is known as 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:

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  1. Decimal Number System
  2. Binary Number System
  3. Octal Number System
  4. Hexadecimal Number System

Lets see about all these number systems in details.



Decimal Number System

The decimal number system consists of ten digits i.e. from 0 to 9. The base of 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 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 × 82 + 4 × 81+ 5 × 80

       = 64 + 32 + 5



       = 10110

Hexadecimal 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 the hexadecimal number system is 16.

For example, convert 26BC16 to decimal.

26BC16 = 2 × 163  6 × 162 + 11 × 161 + 12 × 160

               = 8192 + 1536 + 176 + 12

               = 991610

What are the smallest and the largest six-digit numbers in the Number System?

Smallest six-digit number in the number system – 

The smallest 6 digit number in the number system is 100000.

Explanation – If we subtract -1 from the number it becomes 5 digit number that is 99999 (five digit number). So 100000 is the smallest 6 digit number in the number system.

Smallest 6 digit number = 100000

=> 100000 – 1

=> 99999 (Which is 5 digit number)

So it is proved the 100000 is the smallest 6 digit number in the number system.

Largest six-digit number in the number system – 

The largest 6 digit number in the number system is  – 999999

Explanation – If you add 1 to this number it becomes 1000000 which is a 7 digit number. So 999999 is the largest six digit number in the number system.

Largest 6 digit number in the number system = 999999

= > 999999 + 1  

= > 1000000 (which is 7 digit number)



Hence it is proved that 999999 is the largest six digit number.

Calculate how many number lie between these two values?

We can determine how many numbers lie between the smallest 6-digit number and the largest 6-digit number. We can simply do it by subtracting the smallest number from the largest number. That is –

⇒ 999999 − 100000 = 899999

Hence, total 899999 numbers are lie between the smallest 6-digit number and the largest 6-digit number.

Similar 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 largest 1 digit number?

Answer: 

Largest 1 digit number in the number system 9.

Question 3. Calculate how many number lie between smallest 1 digit number and largest 1 digit number?

Answer:

As we know smallest 1 digit number in the number system is 0 and largest 1 digit number in the number system 9. Therefore total numbers lie between these two numbers are – 

=> 9 – 0 = 9

Hence, total 9 numbers are lie between the smallest 1-digit number and the largest 1-digit number.

Question 4. What is the smallest 3 digit number?

Answer: 

The 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 2 digit number )

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

Question 5. What is the largest 3 digit number ?

Answer:

Largest 3 digit number in the number system 999.

Explanation – If we add +1 to the number ( 999 ) it becomes 4 digit number that is 1000 ( Four digit number ). So 999 is the largest 3 digit number in the number system.

Largest 3 digit number = 999

=> 999 + 1

=> 1000 ( Which is 4 digit number )

So it is proved the 999 is the largest 3 digit number in the number system.

Question 6. 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 7. 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.




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