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

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:

- Decimal Number System
- Binary Number System
- Octal Number System
- 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 :

(1×10

^{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 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 × 8

^{2}+ 4 × 8^{1}+ 5 × 8^{0}= 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 × 16

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